Ronald Graham

Q: What Schools Are Affiliated With Ronald Graham

Ronald Graham is affiliated with the following schools: University of California, Berkeley, Massachusetts General Hospital, Harvard University, University of California, San Diego, Stanford University

Ronald Graham's AcademicInfluence.com Rankings

Mathematics

#55

World Rank

#172

Historical Rank

#21

USA Rank

Combinatorics

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Historical Rank

USA Rank

Graph Theory

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Number Theory

#13

World Rank

#28

Historical Rank

USA Rank

mathematics Degrees

Why Is Ronald Graham Influential?

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By Erik J. Larson, PhD

Graham is Irwin and Joan Jacobs Professor in Computer Science and Engineering at the University of California, San Diego (UCSD). He also holds the title of Chief Scientist at the California Institute for Telecommunications and Information Technology. He received his Ph.D. in Mathematics from the University of California, Berkeley in 1962, and went into research in industry, working at Bell Labs and then AT&T Labs.

Graham is known for using the largest number in a real mathematical proof, which earned him a spot in the Guinness Book of World Records. The so-called Graham number, used as an upper bound in a proof in an area of mathematics known as Ramsey theory, has since been surpassed, but the Graham number is now part of the lore of mathematics. Graham also helped popularize the “Erdos number,” which is the minimum number of co-authored publications connecting directly to one with Erdos as an author. Although not a developed science, the Erdos number does seem to be an informal measurement of someone’s bona fides in mathematical and scientific publications. Graham participates in other “fun” activities outside of his serious work in mathematics—he is a trampolinist and juggler, for instance!

Graham has won many awards during his long career at AT&T Labs, including the American Mathematical Society’s Steele Prize for a lifetime of accomplishment. He is also Fellow of the ACM, and won the Polya Prize, as well as the Euler Prize, both awarded for top mathematical work.

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Featured in Top Influential Mathematicians Today

According to Wikipedia, Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.

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Ronald Graham's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey (1977) (5737)
Concrete mathematics - a foundation for computer science (1991) (2740)
Bounds on Multiprocessing Timing Anomalies (1969) (2366)
An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set (1972) (1727)
Bounds for certain multiprocessing anomalies (1966) (1571)
Handbook of Combinatorics (1995) (1141)
Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms (1974) (913)
On the History of the Minimum Spanning Tree Problem (1985) (781)
Spearman's Footrule as a Measure of Disarray (1977) (648)
Concrete Mathematics, a Foundation for Computer Science (1991) (581)
The Complexity of Computing Steiner Minimal Trees (1977) (577)
Quasi-random graphs (1988) (484)
The steiner problem in phylogeny is NP-complete (1982) (429)
Old and new problems and results in combinatorial number theory (1980) (405)
Some NP-complete geometric problems (1976) (387)
Concrete mathematics - a foundation for computer science (2. ed.) (1994) (364)
On the addressing problem for loop switching (1971) (347)
Resource Constrained Scheduling as Generalized Bin Packing (1976) (340)
On a linear diophantine problem of Frobenius (1972) (326)
On Additive Bases and Harmonious Graphs (1980) (326)
Optimal scheduling for two-processor systems (1972) (317)
Some intersection theorems for ordered sets and graphs (1986) (279)
COMPLEXITY RESULTS FOR BANDWIDTH MINIMIZATION (1978) (275)
Bounds for Multiprocessor Scheduling with Resource Constraints (1975) (264)
Ramsey’s theorem for $n$-parameter sets (1971) (256)
Lower bounds for constant weight codes (1980) (245)
Dense packings of congruent circles in a circle (1998) (217)
The Number of Baxter Permutations (1978) (213)
Distance Matrix Polynomials of Trees (1978) (205)
On the covering radius of codes (1985) (196)
Cardiovascular responses to exercise as functions of absolute and relative work load. (1983) (195)
Worst-case analysis of memory allocation algorithms (1972) (185)
On embedding graphs in squashed cubes (1972) (180)
Drug therapy. Prazosin. (1979) (178)
Paths, Flows, and VLSI-Layout (1990) (167)
Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions (1990) (165)
Unlikelihood that minimal phylogenies for a realistic biological study can be constructed in reasonable computational time (1982) (162)
Universal cycles for combinatorial structures (1992) (161)
Renal alpha-1 and alpha-2 adrenergic receptors: biochemical and pharmacological correlations. (1981) (155)
Ramsey's Theorem for a Class of Categories. (1972) (154)
Performance Guarantees for Scheduling Algorithms (1978) (153)
Apollonian circle packings:number theory (2000) (152)
Prazosin: the first-dose phenomenon. (1976) (149)
A Constructive Solution to a Tournament Problem (1971) (136)
Spurious systolic hypertension in youth (2000) (135)
Role of muscle mass and mode of contraction in circulatory responses to exercise. (1985) (126)
ANTI-PLATELET ACTIVITY OF BETA-ADRENERGIC ANTAGONISTS: INHIBITION OF THROMBOXANE SYNTHESIS AND PLATELET AGGREGATION IN PATIENTS RECEIVING LONG-TERM PROPRANOLOL TREATMENT (1981) (125)
Finding the Convex Hull of a Simple Polygon (1983) (124)
Alpha blocking action of the antihypertensive agent, prazosin. (1977) (123)
Bounds on multiprocessing anomalies and related packing algorithms (1972) (121)
Quasi-Random Hypergraphs (1989) (118)
The Mathematics of Paul Erdős II (1997) (113)
Euclidean Ramsey Theorems I (1973) (111)
The Shortest-Network Problem (1989) (106)
The mathematics of perfect shuffles (1983) (105)
Rudiments of Ramsey theory (1981) (104)
Isometric embeddings of graphs. (1984) (103)
Hypergraphs (2020) (101)
Age, race, diagnosis, and sodium effects on the pressor response to infused norepinephrine. (1987) (101)
Role of renal prostaglandins in sympathetically mediated renin relase in the rat. (1979) (96)
On isometric embeddings of graphs (1985) (95)
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group (2000) (95)
Routing permutations on graphs via matchings (1993) (94)
Similarity of the hemodynamic responses to static and dynamic exercise of small muscle groups. (1981) (93)
Quasi-random set systems (1991) (91)
On sparse graphs with dense long paths. (1975) (90)
On the distance matrix of a tree (1976) (90)
The Elementary Proof of the Prime Number Theorem (2009) (90)
On Packing Squares with Equal Squares (1975) (89)
Renal function during long-term treatment of hypertension with minoxidil: comparison of benign and malignant hypertension. (1980) (88)
Edge-colored complete graphs with precisely colored subgraphs (1983) (88)
Universal Single Transition Time Asynchronous State Assignments (1967) (87)
Floorplan representations: Complexity and connections (2003) (86)
Curved Hexagonal Packings of Equal Disks in a Circle (1997) (85)
Repeated Patterns of Dense Packings of Equal Disks in a Square (1996) (84)
On the distance matrix of a directed graph (1977) (84)
Abnormal cardiovascular regulation in the mitral valve prolapse syndrome. (1983) (84)
Reducing the bias of multitaper spectrum estimates (2007) (83)
On the history of the Euclidean Steiner tree problem (2014) (83)
On the Cover Polynomial of a Digraph (1995) (82)
On the Structure of t-Designs (1980) (81)
Highly irregular graphs (1987) (80)
A NEW BOUND FOR EUCLIDEAN STEINER MINIMAL TREES (1985) (77)
The effect of location and facility demand on the marginal cost of delivered wood chips from energy crops: a case study of the state of Tennessee (1995) (77)
The Radon transform on $Z^k_2$. (1985) (76)
Juggling Drops and Descents (1994) (75)
Statistical Problems Involving Permutations With Restricted Positions (1999) (73)
Quasi-random subsets of Z n (1992) (72)
On induced subgraphs of the cube (1988) (71)
Quasi-random tournaments (1991) (70)
The Largest Small Hexagon (1975) (70)
On graphs with linear Ramsey numbers (2000) (69)
Improving Dense Packings of Equal Disks in a Square (2000) (68)
Random Walks Arising in Random Number Generation (1987) (68)
Sparse Quasi-Random Graphs (2002) (68)
Analysis of greedy approximations with nonsubmodular potential functions (2008) (66)
On subsets of abelian groups with no 3-term arithmetic progression (1987) (65)
On Universal Graphs for Spanning Trees (1983) (64)
Graph Theory, Combinatorics, Algorithms, and Applications (1991) (64)
Covering the Positive Integers by Disjoint Sets of the Form {[n alpha + beta]: n = 1, 2, ...} (1973) (63)
The effects of ischemia, lactic acid and hypertonic sodium chloride on phrenic afferent discharge during spontaneous diaphragmatic contraction (1986) (63)
ON PRIMITIVE GRAPHS AND OPTIMAL VERTEX ASSIGNMENTS (1970) (63)
A theorem on partitions (1963) (62)
On finite 0-simple semigroups and graph theory (1968) (62)
Erdos on Graphs: His Legacy of Unsolved Problems (2001) (61)
On edgewise 2-colored graphs with monochromatic triangles and containing no complete hexagon (1968) (61)
Dense Packings of Equal Disks in an Equilateral Triangle: from 22 to 34 and Beyond (1994) (61)
Quasi‐random graphs with given degree sequences (2008) (60)
Quantitative theorems for regular systems of equations (1988) (60)
Apollonian Circle Packings : Geometry and Group Theory (2005) (59)
Steiner Trees for Ladders (1978) (59)
Problem #7 (1974) (58)
On Multicolor Ramsey Numbers for Complete Bipartite Graphs (1975) (57)
Penny-packing and two-dimensional codes (1990) (56)
Forced Convex n -Gons in the Plane (1998) (56)
A short proof of van der Waerden’s theorem on arithmetic progressions (1974) (55)
On the number of information symbols in difference-set cyclic codes (1966) (55)
Distance Realization Problems with Applications to Internet Tomography (2001) (54)
A Dynamic location problem for graphs (1989) (53)
Influence of dosage and dietary sodium on the first-dose effects of prazosin. (1977) (53)
On Schur Properties of Random Subsets of Integers (1996) (53)
Performance bounds on the splitting algorithm for binary testing (1974) (53)
On graphs which contain all sparse graphs (1982) (51)
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings (2000) (51)
Renal Alpha‐Adrenergic Receptor Abnormality in the Spontaneously Hypertensive Rat (1982) (51)
A Packing Inequality for Compact Convex Subsets of the Plane (1969) (49)
Balanced design of bootstrap simulations (1990) (48)
On graphs which contain all small trees (1978) (47)
A Note on Irregularities of Distribution (2013) (47)
Handbook of combinatorics (vol. 1) (1996) (47)
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions (2000) (45)
Communication latency aware low power NoC synthesis (2006) (44)
Information Bounds Are Weak in the Shortest Distance Problem (1980) (44)
The effect of mental arithmetic in normotensive and hypertensive subjects, and its modification by beta-adrenergic receptor blockade. (1977) (43)
The Analysis of Sequential Experiments with Feedback to Subjects (1981) (42)
Effects of Prazosin and Phentolamine on Arterial Pressure, Heart Rate, and Renin Activity: Evidence in the Conscious Rat for the Functional Significance of the Presynaptic α-Receptor (1979) (42)
Combinatorial designs related to the strong perfect graph conjecture (1979) (41)
DIFFERING EFFECTS OF THE VASODILATOR DRUGS, PRAZOSIN AND DIAZOXIDE ON PLASMA RENIN ACTIVITY IN THE DOG (1976) (40)
On Bipartite Graphs with Linear Ramsey Numbers (2001) (39)
Recent trends in Euclidean Ramsey theory (1994) (39)
Cohomological aspects of hypergraphs (1992) (38)
Some Monotonicity Properties of Partial Orders (1979) (38)
Combinatorics for the East Model (2001) (38)
A Hadamard-Type Bound on the Coefficients of a Determinant of Polynomials (1973) (38)
On sampling with Markov chains (1996) (37)
Minimum steiner trees in normed planes (1993) (37)
Dynamic Search in Graphs (1987) (37)
On permutations containing no long arithmetic progressions (1977) (37)
Some of My Favorite Problems in Ramsey Theory (2006) (36)
On cubical graphs (1975) (36)
Some Results on Matching in Bipartite Graphs (1969) (36)
The graph of generating sets of an abelian group (1999) (35)
Mechanism of the hypotensive action of prazosin. (1977) (35)
L worst-case performance bounds for rumple one-dimensional packing algorithms siam j (1974) (35)
Revisiting floorplan representations (2001) (35)
Complete sequences of polynomial values (1964) (35)
Combinatorics: Ancient and Modern (2013) (34)
Parallelism versus Memory Allocation in Pipelined Router Forwarding Engines (2004) (34)
On Steiner trees for bounded point sets (1981) (34)
The effect of hypertension, sodium, and race on isoproterenol sensitivity. (1988) (33)
Selective alpha 1-adrenergic antagonists: therapeutically relevant antihypertensive agents. (1984) (33)
Haemodynamic responses to static and dynamic handgrip before and after autonomic blockade. (1983) (33)
Combinatorial Designs Related to the Perfect Graph Conjecture (1984) (33)
Guessing secrets (2001) (33)
Edge flipping in graphs (2012) (32)
Steiner Trees on a Checkerboard (1989) (32)
On the bases with an exact order (1980) (31)
Linear Extensions of Partial Orders and the FKG Inequality (1982) (31)
On Finite Sums of Unit Fractions (1964) (31)
A whirlwind tour of computational geometry (1990) (31)
Anti-Hadamard matrices (1984) (31)
Applications of the FKG Inequality and Its Relatives (1982) (30)
The Combinatorial Mathematics of Scheduling (1978) (28)
Some Recent Developments in Ramsey Theory (1975) (28)
Combinatorics: Recent results in graph decompositions (1981) (28)
Haemodynamic effects of prazosin. (1976) (28)
On the Fractional Covering Number of Hypergraphs (1988) (28)
Experience with prazosin in the treatment of patients with severe hypertension. (1976) (27)
Maximal subsemigroups of finite semigroups (1968) (27)
Hemodynamic and Neuroendocrine Responses to Acute and Chronic Alpha‐adrenergic Blockade with Prazosin and Phenoxybenzamine (1983) (26)
On the Set of Common Differences in van der Waerden’s Theorem on Arithmetic Progressions (1999) (26)
Monochromatic Equilateral Right Triangles on the Integer Grid (2006) (26)
Myocardial beta-adrenergic receptors in the stroke-prone spontaneously hypertensive rat. (1980) (26)
Comparative Effects of Prazosin and Phenoxybenzamine on Arterial Blood Pressure, Heart Rate, and Plasma Catecholamines in Essential Hypertension (1979) (26)
Descent polynomials for permutations with bounded drop size (2009) (25)
Bounds for arrays of dots with distinct slopes or lengths (1992) (25)
The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle (1993) (25)
Pebbling a Chessboard (1995) (25)
New bounds on a hypercube coloring problem (2002) (25)
Enumerating split-pair arrangements (2008) (24)
Intersection Theorems for Vector Spaces (1985) (23)
Clinical Pharmacology of Prazosin Used Alone or in Combination in the Therapy of Hypertension (1980) (23)
The Elementary Proof of the Prime (2009) (23)
Worst case bounds for simple one-dimensional packing algorithms (1974) (22)
An affine walk on the hypercube (1992) (22)
A simpler counterexample to the Reconstruction Conjecture for denumerable graphs (1972) (22)
Patterns and Structures in Disk Packings (1997) (22)
On η-valued functionally complete truth functions (1967) (22)
Induced restricted Ramsey theorems for spaces (1987) (22)
Effects of atrial natriuretic factor on blood flow distribution and vascular resistance in conscious dogs. (1991) (22)
Constructing zero-deficiency parallel prefix adder of minimum depth (2005) (22)
Indoramin and prazosin as adjuncts to beta adrenoceptor blockade in hypertension (1979) (21)
Effects of short‐term beta blockade on blood pressure, plasma thromboxane B2, and plasma and urinary prostaglandins E2 and F2α in normal subjects (1982) (21)
Are There n + 2 Points in E n With Odd Integral Distances? (1974) (21)
On the improbability of reaching Byzantine agreements (1989) (21)
Random walks on generating sets for finite groups (1996) (21)
Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks (2011) (21)
Bounds on scheduling with limited resources (1973) (21)
ON THE GROWTH OF A VAN DER WAERDEN-LIKE FUNCTION (2006) (20)
3-D floorplanning using labeled tree and dual sequences (2008) (20)
A Canonical Partition Theorem for Equivalence Relations on Zt (1983) (20)
Combinatorial Scheduling Theory (1978) (20)
On the construction of zero-deficiency parallel prefix circuits with minimum depth (2006) (20)
Primitive Juggling Sequences (2008) (20)
On finite sums of reciprocals of distinct $n$th powers. (1964) (20)
A Note on the Binomial Drop Polynomial of a Poset (1994) (19)
The tight lower bound for the Steiner ratio in Minkowski planes (1994) (19)
Complements and transitive closures (1972) (19)
THE RADON TRANSFORM ON Z (1985) (19)
Quantitative Forms of a Theorem of Hilbert (1985) (19)
Approximately optimal trees for group key management with batch updates (2009) (19)
On A Theorem of Uspensky (1963) (19)
An Upper Bound on Minimum Distance for a k-ary Code (1968) (19)
Saralasin‐Induced Renin Release: Its Blockade by Prostaglandin Synthesis Inhibitors in the Conscious Rat (1979) (18)
A symmetrical Eulerian identity (2010) (18)
Concrete Math (1988) (18)
Single-processor scheduling with time restrictions (2014) (18)
On the prime factors of (²ⁿ_{}) (1975) (18)
Enumerating (Multiplex) Juggling Sequences (2008) (17)
Minimum perimeter rectangles that enclose congruent non-overlapping circles (2004) (17)
On the permanent of Schur's matrix (1976) (17)
Minimal decompositions of graphs into mutually isomorphic subgraphs (1981) (17)
Pursuit - Evasion games on graphs (1988) (17)
Oblivious and Adaptive Strategies for the Majority and Plurality Problems (2005) (17)
Maximizing data locality in distributed systems (2006) (17)
An Irreducibility Criterion for Polynomials Over the Integers (1969) (17)
Lexicographic Ramsey Theory (1993) (16)
A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture (2004) (16)
Finding Patterns Avoiding Many Monochromatic Constellations (2010) (16)
A Tribute to Paul Erdős: On graphs not containing prescribed induced subgraphs (1990) (16)
Maximal antiramsey graphs and the strong chromatic number (1989) (16)
Egyptian Fractions (2013) (16)
On Partitions of En (1980) (16)
ON TIGHTEST PACKINGS IN THE MINKOWSKI PLANE (1972) (16)
Tiling rectangles with rectangles (1982) (16)
Pharmacological evidence for a functional role of the prejunctional alpha-adrenoreceptor in noradrenergic neurotransmission in the conscious rat (1980) (15)
Transient high‐affinity binding of agonists to α1‐adrenergic receptors of intact liver cells (1985) (15)
Card guessing with partial feedback (2020) (15)
A Note on the Intersection Properties of Subsets of Integers (1980) (15)
On Unimodality for Linear Extensions of Partial Orders (1980) (15)
Character design and stamp algorithms for Character Projection Electron-Beam Lithography (2012) (15)
Effects of Clonidine on 24‐Hour Hormonal Secretory Patterns, Cardiovascular Hemodynamics, and Central Nervous Function in Hypertensive Adolescents (1980) (14)
Old and New Problems and Results in Ramsey Theory (2008) (14)
Euclidean Ramsey theorems on the n-sphere (1983) (14)
Guessing about Guessing: Practical Strategies for Card Guessing with Feedback (2020) (14)
Contemporary trends in discrete mathematics : from DIMACS and DIMATIA to the future : DIMATIA-DIMACS conference, May 19-25, 1997, Štiřín Castle, Czech Republic (1999) (14)
On partitions of (1980) (14)
On the permanents of complements of the direct sum of identity matrices (1981) (13)
Constructing Zero-deficiency Parallel Prefix Circuits of Minimum Depth (2005) (13)
Classes of interval graphs under expanding length restrictions (1985) (13)
Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio (2004) (13)
Fault-free Tilings of Rectangles (1981) (13)
Stratified random walks on the n-cube (1997) (13)
Timing Model Reduction for Hierarchical Timing Analysis (2006) (13)
Maximally Nontransitive Dice (2018) (13)
On the Distribution of nθ Modulo 1 (1968) (13)
EFFECT OF INDOMETHACIN ON HYDRALAZINE‐INDUCED RENIN AND CATECHOLAMINE RELEASE IN THE CONSCIOUS RABBIT (1980) (12)
Complete sequences of sets of integer powers (1996) (12)
Anarchy Is Free in Network Creation (2013) (12)
Addition chains with multiplicative cost (1978) (12)
A Fibonacci-like Sequence of Composite Numbers (1964) (12)
Packing equal squares into a large square (2009) (12)
OLD AND NEW PROBLEMS AND RESULTS IN COMBINATORIAL NUMBER THEORY : van der WAERDEN'S THEOREM AND RELATED TOPICS (1980) (12)
The Solutions to Elmsley's Problem (2007) (12)
Selective alpha 1-adrenergic blockade, lipids, and coronary heart disease risk. Considerations in the treatment of mild hypertension. (1989) (11)
ON PRODUCTS OF FACTORIALS BY (1976) (11)
Optimal Tree Structures for Group Key Management with Batch Updates (2007) (11)
Ramsey's theorem for $n$-dimensional arrays (1969) (11)
Unseparated pairs and fixed points in random permutations (2013) (11)
Note on a Nonlinear Recurrence Related to √2 (1970) (11)
50 Years of Combinatorics, Graph Theory, and Computing (2019) (11)
On irregularities of distribution of real sequences. (1981) (11)
Permanental generating functions and sequential importance sampling (2019) (10)
Differences in Response of Black Hypertensives to Alpha vs. Beta Adrenergic Antagonists: Preliminary Findings (1985) (10)
Efficient realization techniques for network flow patterns (1981) (10)
A tight lower bound for the Steiner ratio in Minkowski planes (1995) (10)
Irreducible Apollonian Configurations and Packings (2010) (10)
Combinatorial mathematics : proceedings of the third international conference (1989) (10)
Universal caterpillars (1981) (10)
Guessing secrets with inner product questions (2002) (10)
Generalized Eulerian sums (2012) (10)
Neurogenic Histaminergic Vasodilation in Canine Skeletal Muscle: Mediation by α2‐Adrenoceptor Stimulation (1988) (10)
DEDICATED TO THE MEMORY OF THEODORE S. MOTZKIN (1972) (9)
Products of Universal Cycles (2005) (9)
Effects of prazosin on hemodynamics, hemostasis, and serum lipid and lipoprotein levels in normal and hypercholesterolemic monkeys. (1989) (9)
On extremal density theorems for linear forms (1977) (9)
On minimal colorings without monochromatic solutions to a linear equation (2010) (9)
Bus Matrix Synthesis Based on Steiner Graphs for Power Efficient System-on-Chip Communications (2011) (9)
Restrictions of Minimum Spanner Problems (1997) (9)
OLD AND NEW EUCLIDEAN RAMSEY THEOREMS (1985) (9)
ORIGAMI RINGS (2010) (9)
Universal Juggling Cycles (2006) (8)
Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs (1982) (8)
On sparse sets hitting linear forms (8)
Tiling Polygons with Lattice Triangles (2010) (8)
The Radon transform on Abelian Groups (1987) (8)
Generalized de Bruijn Cycles (2004) (8)
Topics in Euclidean Ramsey Theory (1990) (8)
Inversion-descent polynomials for restricted permutations (2013) (8)
The Steiner ratio for the dual normed plane (1997) (8)
On quadruples of consecutive th power residues (1964) (8)
Beta-adrenoreceptor blockade in the conscious rabbit: effects on plasma renin activity and blood pressure. (1975) (7)
Iterated Triangle Partitions (2010) (7)
Hypercube orientations with only two in-degrees (2010) (7)
On Partitions of an Equilateral Triangle (1967) (7)
On the addressing problem for directed graphs (1985) (7)
Rudiments of Ramsey Theory: Second Edition (2015) (7)
Edge flipping in the complete graph (2015) (7)
Irregularities in the distributions of finite sequences (1970) (7)
A COMBINATORIAL THEOREM FOR PARTIAL SUMS (1963) (7)
On a Diophantine Equation Arising in Graph Theory (1980) (7)
Large minimal sets which force long arithmetic progressions (1986) (6)
On the Prime Factors of \binom2nn (1975) (6)
Juggling card sequences (2015) (6)
Suppression of renin release by timolol. (1976) (6)
Efficient Packings of Unit Squares in a Large Square (2020) (6)
Pursuit- Evasion Games (1988) (6)
A hierarchical three-way interconnect architecture for hexagonal processors (2003) (6)
Open Problems in Euclidean Ramsey Theory (2011) (6)
Combinatorial number theory : proceedings of the 'Integers Conference 2005' in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, October 27-30, 2005 (2007) (5)
alpha 2-Adrenoceptors take centre stage at Nashville meeting. (1996) (5)
On Constant Weight Codes and Harmonious Graphs. (1979) (5)
Plasma substance P levels in normotensive and hypertensive subjects. (1981) (5)
On hypergraphs having evenly distributed subhypergraphs (1993) (5)
On partitions of a finite set (1966) (5)
New bounds on a hypercube coloring problem and linear codes (2001) (5)
Experimental validation of clock synchronization algorithms (1992) (5)
On the Improbability of Reaching Byzantine Agreements (Preliminary Version) (1989) (5)
Homogeneous Collinear Sets in Partitions of Zn (1981) (4)
Single and combined therapy for systemic hypertension with propranolol, hydralazine and hydrochlorothiazide: hemodynamic and neuroendocrine mechanisms of action. (1985) (4)
The Role of Renin in the Antihypertensive Action of β-Adrenoreceptor Blocking Agents (2012) (4)
A general Ramsey product theorem (1979) (4)
Iterated combinatorial density theorems (1990) (4)
Finding Favorites (2003) (4)
Slow Fibonacci walks (2019) (4)
Dense Packings of 3k(k+1)+1 Equal Disks in a Circle for k=1, 2, 3, 4 and 5 (1995) (4)
The Use of Clonidine by Intramuscular Injection in the Treatment of Hypertension * (1977) (4)
The drop polynomial of a weighted digraph (2017) (3)
Corrigendum to "On Isometric Embeddings of Graphs" (1986) (3)
Ramsey Theory in the Work of Paul Erdős (2013) (3)
Subdivision by bisectors is dense in the space of all triangles (2010) (3)
Speculative approaches in hypertension: concepts and drugs of the future. (1981) (3)
Physical synthesis of bus matrix for high bandwidth low power on-chip communications (2010) (3)
On the discrepancy of circular sequences of reals (2016) (3)
Surgical intervention in severe and complicated renal hypertension: Report of the Sydney Renal Hypertension Group (1969-75). (1976) (3)
On the Prime Factors of ( 2 n ) (2004) (3)
Spontaneous Patterns in Disk Packings (1998) (3)
On subgraph number independence in trees (1978) (3)
Binomial coefficient codes over GF(2) (1992) (3)
Pharmacological stimulation of renin secretion within the kidney. (1977) (3)
Proceedings of the third international conference on Combinatorial mathematics (1989) (3)
Constructing Points through Folding and Intersection (2013) (3)
The matrix cover polynomial (2016) (3)
The Mathematics of the Flip and Horseshoe Shuffles (2014) (3)
On a conjecture of Erdös in additive number theory (1964) (3)
Can You Hear the Shape of a Beatty Sequence (2008) (3)
Reflections on a Theme of Ulam (2018) (3)
On complete bipartite subgraphs contained in spanning tree complements (1983) (3)
Explicit error bounds for lattice Edgeworth expansions (2017) (3)
12. The Magic of Charles Sanders Peirce (2019) (3)
Note on a Nonlinear Recurrence Related to $\sqrt{2}$ (1970) (2)
Maximum antichains in the partition lattice (1978) (2)
Optimal jumping patterns (2008) (2)
On the Prime Factors of (2„") (2010) (2)
Monochromatic lines in partitions of Zn (1981) (2)
On Subtrees of Directed Graphs with No Path of Length Exceeding One (1970) (2)
Monochromatic lines in partitions of Zn (1981) (2)
Monochromatic lines in partitions of Zn (1981) (2)
Collapsing numbers in bases 2, 3, and beyond (2012) (2)
How to Play the Majority Game with Liars (2007) (2)
Egyptian Fractions with Each Denominator Having Three Distinct Prime Divisors (2015) (2)
Unrolling Residues to Avoid Progressions (2012) (2)
MINIMAL DECOMPOSITION OF ALL GRAPHS WITH EQUINUMEROUS VERTICES AND EDGES INTO MUTUALLY ISOMORPHIC SUBGRAPHS (1984) (2)
The Solution of a Certain Recurrence (1966) (2)
De Bruijn Sequences with Varying Combs (2014) (2)
On the limit of a recurrence relation (1999) (2)
On the decomposition of lattice-periodic functions (1965) (2)
How to play the Majority game with a liar (2010) (2)
Dynamic location problems with limited look-ahead (2001) (2)
Tree Structures and Algorithms for Physical Design (2018) (2)
A Characterization of Deadlock Free Resource Contentions (1982) (2)
Coefficients of the Inflated Eulerian Polynomial (2015) (2)
Letter: Prazosin in hypertension. (1974) (2)
Juggling Mathematics and Magic (2013) (2)
Inhibition of hydralazine-induced renin release by indomethacin in the rat. (1980) (2)
Paul Erdős and Egyptian Fractions (2013) (2)
Considerations in the long-term treatment of hypertension. (1983) (2)
Balancing the interconnect topology for arrays of processors between cost and power (2002) (2)
Well dispersed sequences in [0,1]d (2018) (2)
ON IRREGULARITIES OF DISTRIBUTION (1984) (1)
Effects of short-term beta blockade on blood pressure, plasma thromboxane B2, and plasma and urinary prostaglandins E2 and F2 alpha in normal subjects. (1982) (1)
On highly non-associative groupoids (1972) (1)
On the Bandwidths of a Graph and its Complement (2004) (1)
Flipping edges and vertices in graphs (2010) (1)
Corrigendum to: “On isometric embeddings of graphs” [Trans. Amer. Math. Soc. 288 (1985), no. 2, 527–536; MR0776391 (86f:05055b)] (1986) (1)
Ramsey Properties of Families of Graphs (2002) (1)
Commercially Viable Bus Services Are Encouraged by Legislation in N.S.W., Australia (1992) (1)
Three-dimensional Floorplan Representations by Using Corner Links and Partial Order (2018) (1)
Some Ramsey-type results for the n-cube (2010) (1)
Some Ramsey results for the n-cube (2008) (1)
Comments on "On the covering radius of codes" [with reply] (1990) (1)
Nomination for Ronald L. Graham for Ams President (2000) (1)
Arithmetic progressions : from Hilbert to Shelah (1989) (1)
N T ] 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory (2003) (1)
3D floorplan representations: Corner links and partial order (2016) (1)
On Levine's notorious hat puzzle (2014) (1)
Subdivision Using Angle Bisectors Is Dense in the Space of Triangles (2013) (1)
Altered Adrenergic Control in Hypercholesterolemia (1987) (1)
Sum sequences modulo n (2018) (1)
Paul Ivan Korner 1925–2012 (2013) (1)
Inserting Plus Signs and Adding (2016) (1)
Chapter 8. Magic in the Book of Changes (2011) (0)
Distance Matrices of Trees. (1975) (0)
Three views of Ramsey theory (1981) (0)
ORNL DAAC WebGIS: A Web-based GIS System for Visualizing and Distributing Biogeochemical and Ecological Datasets (2007) (0)
Universal SingleTransition TimeAsynchronous StateAssignments (1969) (0)
The 100th Birthday of Paul Erdős/Remembering Erdős (2013) (0)
’ llnlikelihood That Minimal Phylogenies fw a Realistic Biolegisal Study Can Be Constructed in Reasonable Computational fime (1982) (0)
[Comparison of the effects of prazosin and phenoxybenzamine on arterial pressure, heart rate and plasma catecolamines in essential arterial hypertension]. (1980) (0)
Commentary 2 (2012) (0)
Shuffling with ordered cards (2010) (0)
Chapter 12. On Secrets (2011) (0)
Coloring, Packing, and Covering (2020) (0)
Rosenberg James. The application of ternary semigroups to the study of n-valued Sheffer functions. Notre Dame journal of formal logic , vol. 10 (1969), pp. 90–94. (1973) (0)
Efficient Packings of Unit Squares in a Large Square (2019) (0)
Proceedings of the International Conference (3rd) on Combinatorial Mathematics Held in New York on 10-14 June 1985. (Annals of the New York Academy of Sciences. Volume 555) (1989) (0)
Singer F. Richard. Some Sheffer functions for M-valued logics. Scripta mathematica, vol. 28 (1967), pp. 21–27. (1969) (0)
Graph Ramsey theory (1981) (0)
Jumping Sequences Steve Butler (2008) (0)
On the discrepancy of linear sequences of reals (2015) (0)
Chapter 3. Is This Stuff Actually Good for Anything (2011) (0)
The American Mathematical Monthly (2018) (0)
N T ] 1 1 Se p 20 00 Apollonian Circle Packings : Number Theory (2000) (0)
About the Spencer (2010) (0)
Ramsey’s theorem (1981) (0)
Combinatorial reconstruction theorems (1992) (0)
Erratum: Quasi‐random graphs with given degree sequences (2008) (0)
Chapter 1. Mathematics in the Air (2011) (0)
A CENTRAL LIMIT THEOREM FOR A NEW STATISTIC ON PERMUTATIONS (2016) (0)
The Passing of Ron Graham (2020) (0)
Chapter 5. From the Gilbreath Principle to the Mandelbrot Set (2011) (0)
The Hales-Jewett theorem (1981) (0)
Review: F. Richard Singer, Some Sheffer Functions for $M$-Valued Logics (1969) (0)
2 Euclidean Ramsey Theory (2016) (0)
Preface to the John Selfridge Memorial Issue (2012) (0)
Maximally Nontransitive (2017) (0)
Chapter 7. The Oldest Mathematical Entertainment (2011) (0)
Review: James Rosenberg, The Application of Ternary Semigroups to the Study of $n$-Valued Sheffer Functions (1973) (0)
The digraph drop polynomial Fan (2017) (0)
Graceful configurations in the plane (1993) (0)
Preliminary ideas. Suppose G is an n-valued truth function of two variables p and q. We shall denote the truth table of G by the linear notation (2016) (0)
Kirin Vladimir G.. On the polynomial representation of operators in the n-valued propositional calculus. Glasnik matematičko-fizički i astronomski (Periodicum mathematico-physicum et astronomicum), ser. 2 vol. 18 (1963), pp. 3–12. (1972) (0)
An Asymptotic Result on a Zero of a Function (1963) (0)
Quasi-Random Combinatorial Structures (Abstract) (1994) (0)
Szemerédi’s theorem (1981) (0)
Appendix a Proof of Theorem 3.1: We Represent the System by a Bipartite Graph Claim 4.2 Every D Gj 2 G Lled during the Rst Stage of a R Unites the Holes Existing in R into A (2011) (0)
Comparison of pharmacologic and biochemical characteristics of renal alpha receptors (1979) (0)
Floorplan Representations : Corner Links and Partial Order (2016) (0)
Recovering permutations over a deletion channel (2017) (0)
Renal Function During Long-Term Treatment of Hypertension with Minoxidil (2020) (0)
LEVEL oc THE ANALYSIS OF SEQUENTIAL EXPERIMENTS WITH FEEDBACK TO SUBJECTS by Persi Diaconis (0)
Paperclip graphs (2019) (0)
Combinatorial Problems Arising in Massive Data Sets (Abstract) (1998) (0)
A Remark on a Paper of Erdős and Nathanson (1996) (0)
Post traumatic renal hypertension. (1984) (0)
Report of the Session on Complexity of Combinatorial Problems (1979) (0)
The theorems of Schur, Folkman, and Hindman (1981) (0)
North-Holland 181 Binomial coefficient codes over W 2 ) (1992) (0)
An interstice relationship for flowers with four petals (2013) (0)
Extremal Graph Theory (2020) (0)
An interstice relationship for flowers with four petals (2013) (0)
Chapter 2. In cycles (2011) (0)
Erratum: Quasi-random graphs with given degree sequences (2008) (0)
Partition and sum is fast (2015) (0)
Erdős Stories as told by Andy Vázsonyi (2020) (0)
Research Courses Undergraduate Graduate News Resources People (2001) (0)
Chapter 6. Neat Shuffles (2011) (0)
Note On Induced Subgraphs of the Cube (1988) (0)
Title Irreducible Apollonian Configurations and Packings Permalink (2010) (0)
Note Universal Caterpillars (1981) (0)
van der Waerden’s theorem (1981) (0)
Review: Richard L. Call, A Minimal Canonically Complete M-Valued Proper Logic for Each M (1970) (0)
Call Richard L.. A minimal canonically complete M-valuedproper logic for each M. The journal of symbolic logic, vol. 33 (1968), pp. 108–110. (1970) (0)
Chapter 9. What Goes Up Must Come Down (2011) (0)
N T / 0 00 91 13 v 2 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory (2005) (0)
Is Randomness Necessary (2011) (0)
Review: Vladimir G. Kirin, On the Polynomial Representation of Operators in the $n$-valued Propositional Calculus (1972) (0)
THE POSITIVE INTEGERS BY DISJOINT SETS (2003) (0)
Rado’s theorem (1981) (0)
Quasi-Random Subsets of Integern (1992) (0)
2] K. Simon, Finding a Minimal Transitive Reduction in a Strongly Connected Digraph With (2007) (0)
Chapter 10. Stars of Mathematical Magic (And some of the best tricks in the book) (2011) (0)
Universal structures Fan Chung cycles for combinatorial (1991) (0)
Principles of Combinatorics (C. Berg) (1972) (0)
A Near-Optimal Algorithm for a Locality Maximising Placement Problem (2004) (0)
PR ] 1 0 O ct 2 02 0 Card Guessing with Partial Feedback (2020) (0)
Chapter 11. Going Further (2011) (0)
Jumping sequences (2008) (0)
Exploration-production studies in newly drilled Devonian-shale gas wells. Annual technical report, February 1, 1987-January 31, 1988 (1988) (0)
Design and Analysis of Transient Fault Tolerance in SRAM with different NT Techniques (2017) (0)
Random Graphs and Graph Enumeration (2020) (0)
. Agency Use Onlyleave Blank 2. Report Date 3. Report Type and Dates Covered Experimental Validation of Clock Synchronization Algorithms (1992) (0)
Chapter 4. Universal Cycles (2011) (0)

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