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Mathematics

D-Index
31
Citations
3242
World Ranking
3384
National Ranking
1324

Overview

Igor Pak is affiliated with the University of California, Los Angeles in the United States. Their research spans primarily the fields of Mathematics and Computer Science, with significant contributions to subfields including Discrete Mathematics and Combinatorics, Computational Theory and Mathematics, Algebra and Number Theory, Geometry and Topology, and Statistics and Probability.

Their work covers main topics such as Advanced Combinatorial Mathematics, Advanced Mathematical Identities, Limits and Structures in Graph Theory, Markov Chains and Monte Carlo Methods, Commutative Algebra and Its Applications, Random Matrices and Applications, and Algebraic Structures and Combinatorial Models.

Igor Pak's frequent publication venues include arXiv (Cornell University), The Electronic Journal of Combinatorics, Transactions of the American Mathematical Society, Algebraic Combinatorics, and Notices of the American Mathematical Society. Their notable recent papers include:

  • Bounds on Kronecker coefficients via contingency tables, 2020, Linear Algebra and its Applications
  • Exact Exponential Algorithms for Two Poset Problems, 2020, arXiv (Cornell University)
  • Counting Linear Extensions of Restricted Posets, 2020, The Electronic Journal of Combinatorics
  • Lower bounds for contingency tables via Lorentzian polynomials, 2022, Israel Journal of Mathematics
  • Introduction to the combinatorial atlas, 2022, Expositiones Mathematicae

Igor Pak has collaborated frequently with several researchers. The most common coauthors include Swee Hong Chan, Greta Panova, Alejandro H. Morales, Christian Ikenmeyer, and Nikita Gladkov.

Best Publications

  • Partition bijections, a survey

    Igor Pak

  • Lifting Markov chains to speed up mixing

    Fang Chen;László Lovász;Igor Pak

  • Log-concavity of the partition function

    Stephen DeSalvo;Igor Pak

  • The product replacement algorithm and Kazhdan’s property (T)

    Alexander Lubotzky;Igor Pak;Igor Pak

  • A direct bijective proof of the hook-length formula

    Jean-Christophe Novelli;Igor Pak;Alexander V. Stoyanovskii

  • WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM

    Igor Pak

  • On non-uniqueness of percolation on nonamenable Cayley graphs *

    Igor Pak;Tatiana Smirnova-Nagnibeda

  • Combinatorics and geometry of Littlewood-Richardson cones

    Igor Pak;Ernesto Vallejo

  • The Kauffman Bracket of Virtual Links and the Bollobás–Riordan Polynomial

    Sergei Chmutov;Igor Pak

  • Hook formulas for skew shapes I. q-analogues and bijections

    Alejandro H. Morales;Igor Pak;Greta Panova

  • Increasing trees and alternating permutations

    A G Kuznetsov;I M Pak;A E Postnikov

  • Four Questions on Birkhoff Polytope

    I. Pak

  • Groups of Intermediate Growth, an Introduction

    Rostislav Grigorchuk;Igor Pak

  • Bijections for refined restricted permutations

    Sergi Elizalde;Igor Pak

  • Hamiltonian paths in Cayley graphs

    Igor Pak;Radoš Radoičić

  • Ribbon tile invariants

    Igor Pak;Igor Pak

  • The product replacement algorithm is polynomial

    I. Pak

  • Hook length formula and geometric combinatorics.

    Igor Pak

  • The shape of random pattern-avoiding permutations

    Sam Miner;Igor Pak

  • Rigidity and polynomial invariants of convex polytopes

    Maksym Fedorchuk;Igor Pak

  • On the complexity of computing Kronecker coefficients

    Igor Pak;Greta Panova

  • Reduced decompositions of permutations in terms of star transpositions, generalized Catalan numbers and k -ARY trees

    Igor Pak

  • Kronecker products, characters, partitions, and the tensor square conjectures

    Igor Pak;Greta Panova;Ernesto Vallejo

  • The Kauffman bracket of virtual links and the Bollob'as-Riordan polynomial

    Sergei Chmutov;Igor Pak

Frequent Co-Authors

Rostislav Grigorchuk
Rostislav Grigorchuk Texas A&M University
Robin Pemantle
Robin Pemantle University of Pennsylvania
László Lovász
László Lovász Eötvös Loránd University
Robert M. Guralnick
Robert M. Guralnick University of Southern California
Cristopher Moore
Cristopher Moore Santa Fe Institute
Don Coppersmith
Don Coppersmith IBM (United States)
László Babai
László Babai University of Chicago
Van Vu
Van Vu Yale University

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