Alan J. Hoffman

Q: What Schools Are Affiliated With Alan J. Hoffman

Alan J. Hoffman is affiliated with the following schools: American University, Columbia University

Alan J. Hoffman's AcademicInfluence.com Rankings

Alan J. Hoffman

Mathematics

#747

World Rank

#1353

Historical Rank

#326

USA Rank

Measure Theory

#593

World Rank

#826

Historical Rank

#242

USA Rank

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Mathematics

Why Is Alan J. Hoffman Influential?

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According to Wikipedia, Alan Jerome Hoffman was an American mathematician and IBM Fellow emeritus, T. J. Watson Research Center, IBM, in Yorktown Heights, New York. He was the founding editor of the journal Linear Algebra and its Applications, and held several patents. He contributed to combinatorial optimization and the eigenvalue theory of graphs. Hoffman and Robert Singleton constructed the Hoffman–Singleton graph, which is the unique Moore graph of degree 7 and diameter 2.

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Alan J. Hoffman'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 Works

On approximate solutions of systems of linear inequalities (1952) (734)
Lower bounds for the partitioning of graphs (1973) (725)
A Characterization of Comparability Graphs and of Interval Graphs (1964) (622)
On Moore Graphs with Diameters 2 and 3 (1960) (461)
The variation of the spectrum of a normal matrix (1953) (367)
Integral Boundary Points of Convex Polyhedra (2010) (285)
On Nonterminating Stochastic Games (1966) (256)
Some metric inequalities in the space of matrices (1955) (248)
A generalization of the Eckart-Young-Mirsky matrix approximation theorem (1987) (201)
On the Polynomial of a Graph (1963) (181)
SOME RECENT APPLICATIONS OF THE THEORY OF LINEAR INEQUALITIES TO EXTREMAL COMBINATORIAL ANALYSIS (2003) (175)
Applications of Graph Theory to Group Structure. (1966) (172)
Totally-Balanced and Greedy Matrices (1985) (153)
Some Properties of Graphs with Multiple Edges (1965) (148)
On the spectral radius of (0,1)-matrices (1985) (146)
A generalization of max flow—min cut (1974) (123)
ON SIMPLE LINEAR PROGRAMMING PROBLEMS (2003) (100)
Maximum degree in graphs of diameter 2 (1980) (98)
Complexity Bounds for Regular Finite Difference and Finite Element Grids (1973) (97)
On balanced matrices (1974) (95)
Systems of inequalities involving convex functions (1957) (91)
On the distance matrix of a directed graph (1977) (84)
On limit points of spectral radii of non-negative symmetric integral matrices (1972) (81)
On the Uniqueness of the Triangular Association Scheme (1960) (78)
Optimal partitions having disjoint convex and conic hulls (1992) (71)
Self-orthogonal latin squares of all orders $n \ne 2,3,6$ (1974) (67)
On graphs whose least eigenvalue exceeds − 1 − √2 (1977) (65)
Line-sum-symmetric scalings of square nonnegative matrices (1985) (60)
Two remarks on compositive matrices (1969) (54)
Approximations to Solutions to Systems of Linear Inequalities (1995) (54)
On Copositive Matrices with - 1, 0, 1 Entries (1973) (54)
Cycling in the Simplex Algorithm (2003) (52)
The polynomial of a directed graph (1965) (43)
On partitions of a partially ordered set (1977) (42)
Eigenvalues and partitionings of the edges of a graph (1972) (37)
On the Exceptional Case in a Characterization of the Arcs of a Complete Graph (1960) (37)
Cyclic Affine Planes (1952) (36)
Partitioning, Spectra and Linear Programming (1984) (34)
ON THE LINE GRAPH OF A SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN (1965) (34)
A note on shortest path, assignment, and transportation problems (1963) (33)
Systems of Distinct Representations and Linear Programming (1956) (32)
On abstract dual linear programs (1963) (29)
Bounds for the spectrum of normal matrices (1994) (28)
A Fast Algorithm that makes Matrices Optimally Sparse (1984) (28)
Lattice Polyhedra II: Generalization, Constructions and Examples (1982) (27)
On the Line Graph of the Complete Bipartite Graph (1964) (27)
PATH PARTITIONS AND PACKS OF ACYCLIC DIGRAPHS (1985) (27)
Aspects of the Traveling Salesman Problem (1984) (27)
On unimodular matrices (1962) (26)
On the nonsingularity of complex matrices (1966) (24)
On greedy algorithms, partially ordered sets, and submodular functions (2003) (24)
On lattice polyhedra III: Blockers and anti-blockers of lattice clutters (1978) (24)
Surveys in combinatorics 1985: On greedy algorithms that succeed (1985) (24)
Local Unimodularity in the Matching Polytope (1978) (23)
Two Remarks on Copositive Matrices* (2001) (23)
Chains in the projective line (1951) (23)
On Transportation Problems with Upper Bounds on Leading Rectangles (1985) (23)
Restrictions and Preassignments in Preemptive open Shop Scheduling (1996) (22)
On the line graph of a projective plane (1965) (20)
On matroid intersections (1981) (20)
ON THE FOUNDATIONS OF INVERSION GEOMETRY (1951) (20)
SELF-ORTHOGONAL LATIN SQUARES (2003) (20)
11. Dilworth’s Theorem on Partially Ordered Sets (1957) (19)
Three Observations on Nonnegative Matrices (1967) (19)
Finding all shortest distances in a directed network (1972) (19)
On the convergence of an integer‐programming process (1963) (18)
Total unimodularity and combinatorial theorems (1976) (18)
Summary Progress Report (1970) (18)
Computational Experience in Solving Linear Programs (2017) (18)
A Remark on the Smoothing Problem (1954) (18)
On the line Graph of a Finite Affine Plane (1965) (18)
Block Design Games (1961) (17)
Lower bounds for the rank and location of the Eigenvalues of a matrix (1953) (17)
Monge and Feasibility Sequences in General Flow Problems (1993) (16)
Ordered Sets and Linear Programming (1982) (15)
Triangulations (tilings) and certain block triangular matrices (1985) (14)
A theorem on inverses of convex sets of real matrices with application to the worst case dc problem (1977) (13)
Extending Greene's Theorem to Directed Graphs (1983) (13)
A characterization of normal matrices (1954) (13)
On the Duals of Symmetric Partially-Balanced Incomplete Block Designs (1963) (12)
Polyhedral combinatorics : dedicated to the memory of D. R. Fulkerson (1978) (12)
Extreme Varieties, Concave Functions and the Fixed Charge Problem (2011) (11)
On the existence of sequences and matrices with prescribed partial sums of elements (1997) (11)
On the solution of the caterer problem (1953) (10)
Series parallel composition of greedy linear programming problems (1993) (10)
A note on almost regular matrices (1995) (10)
The Change in the Least Eigenvalued of the Adjacency Matrix of a Graph Under Imbedding (1969) (10)
Patterns of Dependence in Generalizations of Gerschgorin’s Theorem (1970) (9)
On Spectrally Bounded Graphs (1973) (9)
The Role of Unimodularity in Applying Linear Inequalities to Combinatorial Theorems (1979) (9)
On the nonsingularity of real matrices (1965) (9)
A Note on Cross Ratio (1951) (9)
The edge versus path incidence matrix of series-parallel graphs and greedy packing (2001) (9)
A special class of doubly stochastic matrices (1968) (8)
Bounds on the Largest of Minimum Degree Eigenvalues of Graphs (2010) (8)
Gersgorin variations I: on a theme of Pupkov and Solov'ev☆ (2000) (8)
On the relationship between the Hausdorff distance and matrix distances of ellipsoids (1983) (8)
On greedy algorithms for series parallel graphs (1988) (7)
On the covering of polyhedra by polyhedra (1969) (6)
Variations on a theorem of Ryser (1997) (6)
A Characterization of Nonnegative Box-Greedy Matrices (1996) (6)
On simple combinatorial optimization problems (1992) (6)
On bounds for eigenvalues of real symmetric matrices (1981) (6)
D.R. Fulkerson’s contributions to polyhedral combinatorics (1978) (5)
A Simple Proof of a Generalized Cauchy—Binet Theorem (2016) (5)
What the transportation problem did for me (2007) (5)
Artificial Intelligence based Fraud Agent to Identify Supply Chain Irregularities (2005) (5)
Gersgorin variations II: On themes of Fan and Gudkov (2006) (5)
Greedy packing and series-parallel graphs (1988) (4)
Minimizing a unimodal function of two integer variables (1985) (4)
Staircase transportation problems with superadditive rewards and cumulative capacities (1993) (4)
Linear G-functions † (1975) (4)
On an inequality of Hardy, Littlewood and Polya (1953) (4)
Applications of Ramsey Style Theorems to Eigenvalues of Graphs (1975) (4)
MATHEMATICAL METHODS FOR DECISION MAKING. (1966) (4)
On the line graph of the complete tripartite graph (1977) (3)
A special class of doubly stochastic matrices (1969) (3)
On eigenvalues of symmetric (+1, −1) matrices (1974) (3)
10. On Systems of Distinct Representatives (1957) (3)
On a theorem ofOstrowski andTaussky (1954) (3)
On a game in directed graphs (2002) (3)
On a Problem of Zaks (2001) (3)
On the singularity of matrices (2005) (2)
A characterization of non-negative greedy matrices (1993) (2)
Geršgorin variations III: On a theme of Brualdi and Varga (2008) (2)
Combinatorial aspects of Gerschgorin’s theorem (1971) (2)
On the cone of nonnegative circuits (1986) (2)
COMBINATORICS OF INTERVALS PRELIMINARY VERSION (2003) (2)
A Generalization of the Eckart-Young-Mirsky (1987) (2)
What Olga did for me (1998) (2)
Totally-balanced and greedy matrices : (preprint) (1982) (1)
Bounds for the rank and eigenvalues of a matrix (1968) (1)
Linear Inequalities and Analysis (1964) (1)
A Case for Using Survey Techniques with Children (with Some Reservations). (1975) (1)
Note on a conjecture of Kojima and Saigal (1985) (1)
On signed graphs and gramians (1977) (1)
A nonlinear allocation problem (1994) (1)
SYSTEMS OF INEQUALITIES INVOLVING CONVEX (2010) (1)
On the submodular matrix representation of a digraph (2002) (1)
Aspects of the traveling salesman problem by M . (1)
SYSTEMS OF INEQUALITIES INVOLVING CONVEX FUNCTIONS 1 (2010) (1)
A Special Issue in Memory of George B. Dantzig (2008) (1)
Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices (1997) (1)
Two Remarks on the Mendelsohn-Dulmage Theorem (1982) (1)
Geršgorin variations IV: A left eigenvector approach (2016) (0)
Combinatorial Aspects of Linear Algebra. (1977) (0)
The variable annuity and its possible value to you. (1968) (0)
Preface for advanced discrete optimization techniques for VLSI layout problems (1999) (0)
On the variation of co-ordinates in subspaces (1970) (0)
Linear programming with spheres and hemispheres of objective vectors (1991) (0)
NEAREST $\mathcal{S}$-MATRICES OF GIVEN RANK AND THE RAMSEY PROBLEM FOR EIGENVALUES OF BIPARTITE $\mathcal{S}$-GRAPHS (2003) (0)
Will a Keogh plan really help you? (1968) (0)
A note from LAA’s first editor-in-chief (2008) (0)
Some Properties of the Rank and Invariant Factors of Matrices* (1964) (0)
Large Linear Programs (1962) (0)
with terminal vertex i, ei be the number of edges with initial vertex i. G is said to be strongly regular if di=e,=d, i=1, * * *, n; G is said (2016) (0)
K-REGULAR GRAPH WITH DIAMETER 2 (2015) (0)
On a Game in Directed Graphs (Preprint) (2002) (0)
Elevating the role of finance at Mary Lanning Healthcare. (2013) (0)
AD-776 237 ON BALANCED MATRICES (0)
Covers by polars of arrangements (1990) (0)
ON A CONJECTURE OF A. J. HOFFMAN. II (2010) (0)
How to handle an excess contribution to your Keogh plan. (1968) (0)
A caterer knows that in connection with the meals he has arrang- ed to serve during the next n days, he will need r.(> 0) fresh nap- (2016) (0)
RANKS OF MATRICES AND FAMILIES OF CONES (1967) (0)
SHORTEST PATH, ASSIGNMENT AND TRANSPORTATION PROBLEMS (1963) (0)
ON UNIONS AND INTERSECTIONS OF CONES (2003) (0)
The Pennsylvania Project - A Practical Analysis of the Pennsylvania Rent Withholding Act (1972) (0)
Philip Starr Wolfe (2011) (0)
A proof of the convexity of the range of a nonatomic vector measure using linear inequalities (1994) (0)
Preface (1994) (0)
SOME METRIC INEQUALITIES IN THE SPACE (2016) (0)
Legislative Committee Simulation: Regulation in the Automobile Industry. (1983) (0)

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What Schools Are Affiliated With Alan J. Hoffman?

Alan J. Hoffman is affiliated with the following schools: