Igor Pak | Academic Influence

Igor Pak's AcademicInfluence.com Rankings

Igor Pak

Mathematics

#1807

World Rank

#2888

Historical Rank

#735

USA Rank

Combinatorics

#29

World Rank

#33

Historical Rank

#8

USA Rank

Measure Theory

#2949

World Rank

#3502

Historical Rank

#853

USA Rank

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Mathematics

Igor Pak's Degrees

Bachelors Mathematics Moscow State University

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Why Is Igor Pak Influential?

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According to Wikipedia, Igor Pak is a professor of mathematics at the University of California, Los Angeles, working in combinatorics and discrete probability. He formerly taught at the Massachusetts Institute of Technology and the University of Minnesota, and he is best known for his bijective proof of the hook-length formula for the number of Young tableaux, and his work on random walks. He was a keynote speaker alongside George Andrews and Doron Zeilberger at the 2006 Harvey Mudd College Mathematics Conference on Enumerative Combinatorics.

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Igor Pak'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

Partition bijections, a survey (2006) (147)
Lifting Markov chains to speed up mixing (1999) (125)
Log-concavity of the partition function (2013) (108)
The product replacement algorithm and Kazhdan’s property (T) (2000) (93)
On non-uniqueness of percolation on nonamenable Cayley graphs * (2000) (80)
WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM (2009) (70)
Combinatorics and geometry of Littlewood-Richardson cones (2004) (66)
Bijections for refined restricted permutations (2002) (64)
A direct bijective proof of the hook-length formula (1997) (62)
Hook formulas for skew shapes I. q-analogues and bijections (2015) (61)
The product replacement algorithm is polynomial (2000) (57)
Hamiltonian paths in Cayley graphs (2009) (57)
The shape of random pattern-avoiding permutations (2013) (54)
Groups of Intermediate Growth, an Introduction (2008) (50)
Hook length formula and geometric combinatorics. (2001) (49)
The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial (2006) (49)
Strict unimodality of q-binomial coefficients (2013) (47)
Rigidity and polynomial invariants of convex polytopes (2005) (45)
Increasing trees and alternating permutations (1994) (44)
Four Questions on Birkhoff Polytope (2000) (43)
Reduced decompositions of permutations in terms of star transpositions, generalized Catalan numbers and k-ARY trees (1999) (42)
Ribbon tile invariants (2000) (40)
Fast Constructive Recognition of a Black Box Group Isomorphic to Sn or An using Goldbach's Conjecture (2000) (40)
Kronecker products, characters, partitions, and the tensor square conjectures (2013) (37)
Groups of oscillating intermediate growth (2011) (34)
Strong bias of group generators: an obstacle to the “product replacement algorithm” (2000) (33)
Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings (2003) (31)
On Growth of Grigorchuk Groups (2001) (31)
Asymptotics of the number of standard Young tableaux of skew shape (2016) (30)
Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications (2016) (30)
Non-commutative extensions of the MacMahon Master Theorem (2006) (29)
Rapidly Mixing Random Walks and Bounds on Characters of the Symmetric Group (2002) (29)
Hook formulas for skew shapes III. Multivariate and product formulas (2017) (29)
Expansion Of Product Replacement Graphs (2002) (29)
The area of cyclic polygons: Recent progress on Robbins' conjectures (2004) (27)
Acute triangulations of polyhedra and ℝN (2009) (27)
On the complexity of computing Kronecker coefficients (2014) (27)
On Probability Of Generating A Finite Group (1999) (26)
Random Walks On Finite Groups With Few Random Generators (1999) (26)
Counting Linear Extensions of Restricted Posets (2018) (26)
A combinatorial proof of the Rogers-Ramanujan and Schur identities (2004) (25)
Reductions of Young Tableau Bijections (2004) (25)
PERCOLATION ON GRIGORCHUK GROUPS (2001) (24)
Generalized loop‐erased random walks and approximate reachability (2014) (24)
Hook formulas for skew shapes (2015) (24)
Bounds on certain classes of Kronecker and q-binomial coefficients (2017) (24)
Groups of Intermediate Growth: an Introduction for Beginners (2006) (24)
On the largest Kronecker and Littlewood-Richardson coefficients (2018) (23)
The weighted hook length formula (2010) (23)
Unimodality via Kronecker products (2013) (23)
On Kazhdan constants and mixing of random walks (2002) (22)
Tile invariants: new horizons (2003) (21)
Partition congruences by involutions (2004) (21)
Tilings of rectangles with T-tetrominoes (2004) (21)
The Complexity of Generalized Domino Tilings (2013) (21)
Complexity problems in enumerative combinatorics (2018) (20)
A generalization of Sylvester's identity (1998) (20)
On sampling generating sets of finite groups and product replacement algorithm: extended abstract (1999) (19)
Combinatorial evaluations of the Tutte polynomial (2003) (19)
Tiling simply connected regions with rectangles (2013) (19)
On Fine’s Partition Theorems, Dyson, Andrews, And Missed Opportunities (2003) (18)
Tree and Forest Volumes of Graphs (2000) (17)
When and how n choose k (1998) (17)
Bounds on the Kronecker coefficients (2014) (17)
Inflating the Cube Without Stretching (2006) (16)
Partition identities and geometric bijections (2004) (16)
INFLATING POLYHEDRAL SURFACES (2006) (16)
Ribbon Tile Invariants from the Signed Area (2002) (15)
On mixing of certain random walks, cutoff phenomenon and sharp threshold of random matroid processes (2001) (15)
History of Catalan numbers (2014) (15)
Covariants of the symmetric group and its analogs in Weyl algebras (1990) (15)
The Expected Shape of Random Doubly Alternating Baxter Permutations (2014) (15)
The discrete square peg problem (2008) (15)
AN ALGEBRAIC EXTENSION OF THE MACMAHON MASTER THEOREM (2006) (15)
Pattern avoidance is not P-recursive (2015) (14)
Quantum cohomology of Hilbn(C2) and the weighted hook walk on Young diagrams (2012) (14)
On the Number of Faces of Certain Transportation Polytopes (2000) (13)
Mixing time and long paths in graphs (2002) (13)
Short Presburger Arithmetic Is Hard (2017) (12)
Breaking down the reduced Kronecker coefficients (2020) (12)
Random Cayley Graphs with O(log[G]) Generators Are Expanders (1999) (12)
Fast Domino Tileability (2015) (12)
Words in Linear Groups, Random Walks, Automata and P-Recursiveness (2015) (12)
Trees Associated with the Motzkin Numbers (1996) (12)
Complexity of short Presburger arithmetic (2017) (12)
Two Random Walks on Upper Triangular Matrices (2000) (11)
Enumeration of spanning trees of certain graphs (1990) (11)
On Tilings by Ribbon Tetrominoes (1999) (11)
Long cycles in abc-permutations (2008) (11)
Phase transition in random contingency tables with non-uniform margins (2019) (11)
On a question of B. H. Neumann (2002) (10)
Combinatorial inequalities (2019) (10)
On Higman's $k(U_n(\mathbb{F}_q))$ conjecture (2015) (10)
The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs (2004) (10)
On The Graph Of Generating Sets Of A Simple Group (1999) (9)
Lower bounds for contingency tables via Lorentzian polynomials (2020) (9)
The nature of partition bijections I. Involutions (2004) (9)
Bounds on Kronecker coefficients via contingency tables (2020) (8)
Constructing Uniquely Realizable Graphs (2013) (8)
What is in #P and what is not? (2022) (8)
Random walk on upper triangular matrices mixes rapidly (2000) (8)
Asymptotics of principal evaluations of Schubert polynomials for layered permutations (2018) (8)
PROFILES OF INFLATED SURFACES (2009) (8)
Log smoothness and polystability over valuation rings (2018) (8)
On Sampling Integer Points In Polyhedra (2002) (8)
Cayley compositions, partitions, polytopes, and geometric bijections (2014) (8)
Counting With Irrational Tiles (2014) (7)
THE NATURE OF PARTITION BIJECTIONS II. ASYMPTOTIC STABILITY (2004) (7)
A bijective proof of the hook-length formula and its analogs (1992) (7)
Permutation patterns are hard to count (2016) (7)
Extensions of the Kahn-Saks inequality for posets of width two (2021) (7)
What is a combinatorial interpretation? (2022) (7)
Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings (2018) (7)
Limit Shapes via Bijections (2016) (7)
RANDOM WALKS ON NILPOTENT GROUPS (2001) (6)
Presburger Arithmetic with algebraic scalar multiplications (2018) (6)
ENUMERATION OF TREES AND ONE AMAZING REPRESENTATION OF THE SYMMETRIC GROUP (1995) (6)
The cross-product conjecture for width two posets (2021) (6)
Geometry and complexity of O'Hara's algorithm (2007) (6)
Percolation on Finite Cayley Graphs (2002) (6)
Why Is Pi Less Than Twice Phi? (2018) (6)
ENUMERATION OF SPANNING TREES OF GRAPHS (1994) (5)
HOW TO CUT OUT A CONVEX POLYHEDRON (2009) (5)
Enumerating Projections of Integer Points in Unbounded Polyhedra (2016) (5)
Triangulations of Cayley and Tutte polytopes (2011) (5)
Positivity of the symmetric group characters is as hard as the polynomial time hierarchy (2022) (5)
Enumeration of Integer Points in Projections of Unbounded Polyhedra (2016) (5)
A Quantitative Steinitz Theorem for Plane Triangulations (2013) (5)
Testing commutativity of a group and the power of randomization (2012) (5)
COMPLEXITY OF SHORT GENERATING FUNCTIONS (2017) (5)
A short proof of rigidity of convex polytopes (2006) (5)
Acute triangulations of polyhedra and the Euclidean space (2010) (5)
The computational complexity of integer programming with alternations (2017) (5)
Bounds on Kronecker and $q$-binomial coefficients (2014) (5)
Growth in product replacement graphs (2013) (5)
Kirszbraun-type theorems for graphs (2017) (5)
Sorting probability for large Young diagrams (2020) (4)
Using stopping times to bound mixing times (1999) (4)
CONCRETE POLYTOPES MAY NOT TILE THE SPACE (2020) (4)
On the number of contingency tables and the independence heuristic (2020) (4)
CONVERGENCE OF KAC ’ S RANDOM WALK (2007) (4)
Computational complexity and decidability of tileability (2013) (4)
Percolation on Finite Cayley Graphs (2006) (3)
VOLUME-PRESERVING PL-MAPS BETWEEN POLYHEDRA (2004) (3)
Kronecker coefficients: the tensor square conjecture and unimodality (2014) (3)
Bounds on the largest Kronecker and induced multiplicities of finite groups (2018) (3)
Hidden Symmetries of Weighted Lozenge Tilings (2020) (3)
PERIODIC PERMUTATIONS AND THE ROBINSON–SCHENSTED CORRESPONDENCE (2003) (3)
Log-concave poset inequalities (2021) (3)
How to Write a Clear Math Paper: Some 21st Century Tips (2018) (2)
On the Longest $k$-Alternating Subsequence (2014) (2)
Oscillating Tableaux , S p × S q-modules , and Robinson-Schensted-Knuth correspondence Extended (1998) (2)
Resolutions forSn-Modules, associated with Rim Hooks, and combinatorial applications (1994) (2)
Acute triangulations of polyhedra and ℝN (2012) (2)
Effective poset inequalities (2022) (2)
Durfee squares, symmetric partitions and bounds on Kronecker coefficients (2022) (2)
Bijecting hidden symmetries for skew staircase shapes (2021) (2)
Upper bounds on Kronecker coefficients with few rows. (2020) (2)
WHY IS π < 2 φ ? (2016) (2)
Correlation inequalities for linear extensions (2022) (1)
Introduction to the combinatorial atlas (2022) (1)
Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups (2022) (1)
Sorting probability of Catalan posets (2020) (1)
Hook Inequalities (2019) (1)
Collapsing Walls Theorem (2012) (1)
On Finite Geometric Random Walks and Probabilistic Combinatorics (1998) (1)
VC-Dimensions of Short Presburger Formulas (2017) (1)
On the Odd Area of Planar Sets (2016) (1)
Cutoff for biased transpositions (2017) (1)
Domes over Curves (2020) (1)
Lifts, derandomization, and diameters of Schreier graphs of Mealy automata (2014) (1)
TWO RANDOM WALKS ON UPPER TRIANGULAR MATRICESIgor PakDepartment of MathematicsYale UniversityNew Haven (1998) (0)
Lifts, derandomization, and diameters of Schreier graphs of Mealy automata (2017) (0)
Multivariate correlation inequalities for $P$-partitions (2022) (0)
Non-commutative extensions of classical determinantal identities (2007) (0)
COMPUTING THE NUMBER OF FACES OF TRANSPORTATION POLYTOPES IN POLYNOMIAL TIME (1999) (0)
On the Number of Integer Points in Translated and Expanded Polyhedra (2018) (0)
The combinatorics and complexity of integer sequences (2017) (0)
THE NATURE OF PARTITION (2003) (0)
Weighted branching formulas for the hook lengths (2010) (0)
MIXING OF FINITE GEOMETRIC RANDOM WALKS AND THE CUTOFF PHENOMENON (2015) (0)
HOW TO TELL A GOOD MATHEMATICAL STORY (2021) (0)
Number Theory and Combinatorics (2018) (0)
Cayley and Tutte polytopes (2012) (0)
Hook formulas for skew shapes ( extended abstract ) (2016) (0)
Short Stories: Combinatorial Inequalities (2019) (0)
Transversal matroids and strata on Grassmannians (1995) (0)
Complexity of O'Hara's Algorithm (2010) (0)
Fast Domino Tileability (2016) (0)
The Unity of Combinatorics Reviewed by Igor Pak (2021) (0)
VC-Dimensions of Short Presburger Formulas (2019) (0)
Hook Inequalities (2019) (0)
Mathematisches Forschungsinstitut Oberwolfach Report No . 4 / 2007 Geometric and Topological Combinatorics Organised (2007) (0)
NOTE Trees Associated with the Motzkin Numbers (1996) (0)
Growth in product replacement graphs of Grigorchuk groups (2015) (0)
Skyscraper polytopes and realizations of plane triangulations (2017) (0)
Log-Concavity in Planar Random Walks (2021) (0)

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