Pak, Igor - Department of Mathematics, University of California at Los Angeles

• BIJECTIONS FOR REFINED RESTRICTED PERMUTATIONS SERGI ELIZALDE AND IGOR PAK
• Strong bias of group generators: an obstacle to the ``product replacement algorithm''
• COMBINATORICA Bolyai Society Springer-Verlag
• PARTITION IDENTITIES AND GEOMETRIC BIJECTIONS Department of Mathematics, MIT
• Uspekhi Mat. Nauk 49:6 (1994), 79-110 Russian Math. Surveys 49:6 (1994), 79-114 Increasing trees and alternating permutations(1)
• 72 . . , . . d(M) -
• RIGIDITY AND POLYNOMIAL INVARIANTS OF CONVEX POLYTOPES MAKSYM FEDORCHUK AND IGOR PAK
• THE COLLAPSING WALLS THEOREM AND ROM PINCHASI
• HAMILTONIAN PATHS IN CAYLEY GRAPHS Department of Mathematics
• RANDOM WALKS ON NILPOTENT GROUPS Alexander Astashkevich
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• , 2006. 47, 4 514.172.45+514.752.435+519.173
• C. R. Acad. Sci. Paris, t. 330, Srie I, p. 495500, 2000 Probabilits/Probability Theory
• Groups of Intermediate Growth, an Introduction Rostislav Grigorchuk
• On growth of Grigorchuk groups Roman Muchnik, Igor Pak
• INFLATING THE CUBE WITHOUT STRETCHING Consider the surface S of a unit cube C in R 3 . Think of S being a container made
• 220 Communications of the Moscow Mathematical Society Enumeration of spanning trees of certaingraphs
• A GENERALIZATION OF SYLVESTER'S IDENTITY Department of Mathematics
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• INFLATING THE CUBE WITHOUT STRETCHING Consider the surface S of a unit cube C in R3
• Oscillating Tableaux, S p modules, and
• doi: 10.1006/jsco.1999.0295 Available online at http://www.idealibrary.com on
• NON-COMMUTATIVE EXTENSIONS OF THE MACMAHON MASTER THEOREM
• TREES ASSOCIATED WITH THE MOTZKIN NUMBERS Alexander Kuznetsov
• TILE INVARIANTS: NEW HORIZONS Department of Mathematics
• On a question of B.H. Neumann Robert Guralnick
• RANDOM WALKS ON FINITE GROUPS WITH FEW RANDOM GENERATORS
• RIBBON TILE INVARIANTS FROM SIGNED AREA Cristopher Moore
• Mixing time and long paths in graphs We prove that regular graphs with large degree and
• PERCOLATION ON GRIGORCHUK Roman Muchnik and Igor Pak
• PERIODIC PERMUTATIONS AND THE ROBINSON--SCHENSTED CORRESPONDENCE
• THE PRODUCT REPLACEMENT GRAPH ON GENERATING TRIPLES OF PERMUTATIONS
• TESTING COMMUTATIVITY OF A GROUP AND THE POWER OF RANDOMIZATION
• On Kazhdan Constants and Mixing of Random Department of Mathematics
• THE PRODUCT REPLACEMENT ALGORITHM AND KAZHDAN'S PROPERTY (T)
• On sampling generating sets of finite groups and product replacement algorithm. (Extended Abstract)
• Discrete Mathematics and Theoretical Computer Science 1, 1997, 5367 A direct bijective proof of the hook-length
• RANDOM WALKS ON GROUPS: STRONG UNIFORM TIME APPROACH
• TWO RANDOM WALKS ON UPPER TRIANGULAR MATRICES Department of Mathematics
• ON SAMPLING INTEGER POINTS IN POLYHEDRA Department of Mathematics,
• ON THE GRAPH OF GENERATING SETS OF A SIMPLE GROUP
• RAPIDLY MIXING RANDOM WALKS AND BOUNDS ON CHARACTERS OF THE SYMMETRIC GROUP
• Lifting Markov Chains to Speed up Mixing
• TWO RANDOM WALKS ON UPPER TRIANGULAR MATRICES Department of Mathematics
• PERIODIC PERMUTATIONS AND THE ROBINSONSCHENSTED CORRESPONDENCE
• / 0097-3165/02 $35.00 2002 Elsevier Science (USA)
• ENUMERATION OF TREES AND ONE AMAZING REPRESENTATION OF THE SYMMETRIC GROUP
• EXPANSION OF PRODUCT REPLACEMENT GRAPHS Alexander Gamburd
• Reductions of Young tableau bijections Massachusetts Institute of Technology
• ON PROBABILITY OF GENERATING A FINITE GROUP Department of Mathematics
• RIGIDITY AND POLYNOMIAL INVARIANTS OF CONVEX POLYTOPES MAKSYM FEDORCHUK # AND IGOR PAK #
• Tilings of rectangles with Ttetrominoes Michael Korn and Igor Pak
• AN ALGEBRAIC EXTENSION OF THE MACMAHON MASTER PAVEL ETINGOF # AND IGOR PAK #
• Combinatorial evaluations of the Tutte polynomial Michael Korn and Igor Pak
• Discrete Mathematics 204 (1999) 329335 www.elsevier.com/locate/disc
• ON THE NUMBER OF FACES OF CERTAIN TRANSPORTATION POLYTOPES
• GEOMETRY AND COMPLEXITY OF O'HARA'S ALGORITHM MATJA Z KONVALINKA AND IGOR PAK
• THE AREA OF CYCLIC POLYGONS: RECENT PROGRESS ON ROBBINS' CONJECTURES
• Tilings of rectangles with T-tetrominoes Michael Korn and Igor Pak
• Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 1999
• REDUCED DECOMPOSITIONS OF PERMUTATIONS IN TERMS OF STAR TRANSPOSITIONS, GENERALIZED
• Combinatorics and geometry of LittlewoodRichardson cones
• On sampling generating sets of finite groups and product replacement algorithm. (Extended Abstract)
• Journal of Algorithms 50 (2004) 215231 www.elsevier.com/locate/jalgor
• Using stopping times to bound mixing times # October 31, 2004
• J. Symbolic Computation (1999) 11, 1--000 Fast constructive recognition of a black box group
• A SHORT PROOF OF RIGIDITY OF CONVEX POLYTOPES Abstract. We present a much simplified proof of Dehn's theorem on the infini
• The product replacement algorithm is polynomial Igor Pak \Lambda
• 1990, . 24, . 3, 9--13 1.
• Mixing time and long paths in graphs We prove that regular graphs with large degree and
• METRIC COMBINATORICS OF CONVEX POLYHEDRA: CUT LOCI AND NONOVERLAPPING UNFOLDINGS
• Noncommutative Lagrange Theorem and Inversion Polynomials Igor Pak, Alexander Postnikov, Vladimir Retakh
• FOUR QUESTIONS ON BIRKHOFF POLYTOPE Department of Mathematics,
• LONG CYCLES IN ABC--PERMUTATIONS IGOR PAK # AND AMANDA REDLICH #
• GEOMETRY AND COMPLEXITY OF O'HARA'S ALGORITHM MATJAZ KONVALINKA AND IGOR PAK
• Combinatorial evaluations of the Tutte polynomial Michael Korn and Igor Pak
• Combinatorics and geometry of Littlewood-Richardson cones
• ON FINE'S PARTITION THEOREMS, DYSON, ANDREWS, AND MISSED OPPORTUNITIES
• CONVERGENCE OF KAC'S RANDOM WALK AND SERGIY SIDENKO
• DIMACS Technical Report 200003 January 2000
• Combinatorial evaluations of the Tutte polynomial Michael Korn and Igor Pak
• On Kazhdan Constants and Mixing of Random Department of Mathematics
• On tilings by ribbon tetrominoes Roman Muchnik, Igor Pak
• RANDOM WALK ON UPPER TRIANGULAR MATRICES MIXES RAPIDLY
• A direct bijective proof of the hooklength JeanChristophe Novelli \Lambda
• PARTITION BIJECTIONS, A SURVEY Abstract. We present an extensive survey of bijective proofs of classical par-
• A COMBINATORIAL PROOF OF THE ROGERS-RAMANUJAN AND SCHUR IDENTITIES
• RAPIDLY MIXING RANDOM WALKS AND BOUNDS ON CHARACTERS OF THE SYMMETRIC GROUP
• Zentralblatt MATH Database 1931 2002 c 2002 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
• Constructing Uniquely Realizable Graphs and Dan Vilenchik
• INFLATING POLYHEDRAL SURFACES Abstract. We prove that all polyhedral surfaces in R3
• THE NATURE OF PARTITION BIJECTIONS II. ASYMPTOTIC STABILITY
• Acute triangulations of polyhedra and Rn Eryk Kopczyski, Igor Pak
• Acute triangulations of polyhedra and Rn Eryk Kopczyski, Igor Pak
• HOW TO CUT OUT A CONVEX POLYHEDRON AND ROM PINCHASI
• PROFILES OF INFLATED SURFACES IGOR PAK AND JEAN-MARC SCHLENKER
• A SHORT PROOF OF RIGIDITY OF CONVEX POLYTOPES Abstract. We present a much simplified proof of Dehn's theorem on the infini-
• THE AREA OF CYCLIC POLYGONS: RECENT PROGRESS ON ROBBINS' CONJECTURES
• METRIC COMBINATORICS OF CONVEX POLYHEDRA: CUT LOCI AND NONOVERLAPPING UNFOLDINGS
• Annals of Combinatorics 4 (2000) 83-90 0218 0006/00/01083 8$1.50 + 0.20/0
• Functional Analysis and Its Applications, Vol. 29, No. 2, 1995 Transversal Matroids and Strata on Grassmannians
• Journal of Combinatorial Theory, Series A 88, 188 193 (1999) On Tilings by Ribbon Tetrominoes1
• Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2002
• AN ALGEBRAIC EXTENSION OF THE MACMAHON MASTER PAVEL ETINGOF AND IGOR PAK
• Formal Power Series and Algebraic Combinatorics Nankai University, Tianjin, China, 2007
• BIJECTIONS FOR REFINED RESTRICTED PERMUTATIONS SERGI ELIZALDE AND IGOR PAK
• journal of combinatorial theory, Series A 76, 145 147 (1996) Trees Associated with the Motzkin Numbers
• A Bijective Proof of the Hook-Length Formula and its Analogs I. M. Pak and A. V. Stoyanovskii UDC 517
• 5. The author is grateful to W. N. Everitt for drawing his attention to the close connection of Theorem 2 with the results obtained in [6] and to M. Sh. Birman for useful comments concerning this theorem.
• COVARIANTS OF THE SYMMETRIC GROUP AND ITS ANALOGS IN WEYL ALGEBRAS A. A. Kirillov and I. M. Pak UDC 519.45
• THE NATURE OF PARTITION BIJECTIONS I. INVOLUTIONS. Department of Mathematics, MIT
• Previous Up Next Article From References: 10
• ON FINE'S PARTITION THEOREMS, DYSON, ANDREWS, AND MISSED OPPORTUNITIES
• Dedicated to Askold Khovanskii on the occasion of his 60th birthday THE KAUFFMAN BRACKET OF VIRTUAL LINKS AND THE
• MIXING TIME AND LONG PATHS IN GRAPHS Department of Mathematics, MIT
• Using stopping times to bound mixing times October 31, 2004
• HAMILTONIAN PATHS IN CAYLEY GRAPHS Department of Mathematics
• EXPANSION OF PRODUCT REPLACEMENT GRAPHS Alexander Gamburd
• WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM?
• Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2002
• WHEN AND HOW n CHOOSE k Abstract. We discuss different ways of generating k-subsets of an n-set, as well as
• ON NON-UNIQUENESS OF PERCOLATION ON NONAMENABLE CAYLEY GRAPHS
• ON THE GRAPH OF GENERATING SETS OF A SIMPLE GROUP
• Zentralblatt-MATH 1931 -2000 Oc European Mathematical Society, FIZ Karlsruhe & Springer-Verlag Berlin-Heide*
• RANDOM WALKS ON NILPOTENT GROUPS Alexander Astashkevich
• Combinatorics and geometry of Littlewood-Richardson cones
• The product replacement algorithm is polynomial Igor Pak*
• THE AREA OF CYCLIC POLYGONS: RECENT PROGRESS ON ROBBINS' CONJECTURES
• ON THE NUMBER OF FACES OF CERTAIN TRANSPORTATION POLYTOPES
• PARTITION IDENTITIES AND GEOMETRIC BIJECTIONS Igor Pak
• PERCOLATION ON GRIGORCHUK GROUPS
• On sampling generating sets of finite groups Sergey Bratus*, Igor Paky
• On sampling generating sets of finite groups and product replacement algorithm. (Extended Abstract)
• Strong bias of group generators: an obstacle to the "product replacement algorithm"
• A COMBINATORIAL PROOF OF THE ROGERSRAMANUJAN AND SCHUR IDENTITIES
• HOOK LENGTH FORMULA AND GEOMETRIC COMBINATORICS
• NONCOMMUTATIVE EXTENSIONS OF THE MACMAHON MASTER THEOREM
• RANDOM WALKS ON GROUPS: STRONG UNIFORM TIME APPROACH
• ON NONUNIQUENESS OF PERCOLATION ON NONAMENABLE CAYLEY GRAPHS
• Reductions of Young tableau bijections Massachusetts Institute of Technology
• Partition congruences by involutions Christine Bessenrodt
• MIXING TIME AND LONG PATHS IN GRAPHS Department of Mathematics, MIT
• Strong bias of group generators: an obstacle to the ``product replacement algorithm''
• ON MIXING OF CERTAIN RANDOM WALKS, CUTOFF PHENOMENON AND SHARP
• Results from MathSciNet: Mathematical Reviews on the Web Copyright American Mathematical Society 2002
• RIBBON TILE INVARIANTS Email: pak@math.mit.edu
• VOLUMEPRESERVING PLMAPS BETWEEN POLYHEDRA ANDRE HENRIQUES # AND IGOR PAK #
• On sampling generating sets of finite groups Sergey Bratus \Lambda , Igor Pak y
• EXPANSION OF PRODUCT REPLACEMENT GRAPHS Alexander Gamburd
• Partition congruences by involutions Christine Bessenrodt
• WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM?
• On a question of B.H. Neumann Robert Guralnick
• LONG CYCLES IN ABCPERMUTATIONS AND AMANDA REDLICH
• RANDOM WALKS ON NILPOTENT GROUPS Alexander Astashkevich
• JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
• Digital Object Identifier (DOI) 10.1007/s004400000055 Probab. Theory Relat. Fields 117, 407417 (2000)
• Lifting Markov Chains to Example 1.1 It is easy to see that for* * the random
• HAMILTONIAN PATHS IN CAYLEY GRAPHS Igor Pak
• AN ALGEBRAIC EXTENSION OF THE MACMAHON MASTER THEOREM
• On growth of Grigorchuk groups Roman Muchnik, Igor Pak
• J. Symbolic Computation (1999) 11, 1-000 Fast constructive recognition of a black box group
• RAPIDLY MIXING RANDOM WALKS AND BOUNDS ON CHARACTERS OF THE SYMMETRIC GROUP
• WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM?
• TREES ASSOCIATED WITH THE MOTZKIN NUMBERS Alexander Kuznetsov
• RANDOM WALKS ON FINITE GROUPS WITH FEW RANDOM GENERATORS
• Using stopping times to bound mixing times * Igor Paky
• EXPANSION OF PRODUCT REPLACEMENT GRAPHS Alexander Gamburd
• TWO RANDOM WALKS ON UPPER TRIANGULAR MATRICES Igor Pak
• EXPANSION OF PRODUCT REPLACEMENT GRAPHS Alexander Gamburd
• FOUR QUESTIONS ON BIRKHOFF POLYTOPE Igor Pak
• VOLUME-PRESERVING PL-MAPS BETWEEN POLYHEDRA ANDRE HENRIQUES AND IGOR PAK
• Article No. 10.1006/eujc.1999.0392 Available online at http://www.idealibrary.com on
• Dedicated to Askold Khovanskii on the occasion of his 60th birthday THE KAUFFMAN BRACKET OF VIRTUAL LINKS AND THE
• THE NATURE OF PARTITION BIJECTIONS I. INVOLUTIONS. Department of Mathematics, MIT
• Combinatorial evaluations of the Tutte polynomial Michael Korn and Igor Pak
• PARTITION IDENTITIES AND GEOMETRIC BIJECTIONS Department of Mathematics, MIT
• WHEN AND HOW n CHOOSE k Abstract. We discuss different ways of generating ksubsets of an nset, as well as
• Strong bias of group generators: an obstacle to the "product replacement algorithm"
• Results from MathSciNet: Mathematical Reviews on the Web cO Copyright American Mathematical Society 2002
• MIXING TIME AND LONG PATHS IN GRAPHS Igor Pak
• On Kazhdan Constants and Mixing of Random Walks
• RANDOM WALK ON UPPER TRIANGULAR MATRICES MIXES RAPIDLY
• ON PROBABILITY OF GENERATING A FINITE GROUP Igor Pak
• Mixing time and long paths in graphs Igor Pak*
• On a question of B.H. Neumann Robert Guralnick
• WHEN AND HOW n CHOOSE k Igor Pak
• RIBBON TILE INVARIANTS Igor Pak
• ENUMERATION OF TREES AND ONE AMAZING REPRESENTATION OF THE SYMMETRIC GROUP
• Noncommutative Lagrange Theorem and Inversion Polynomials Igor Pak, Alexander Postnikov, Vladimir Retakh
• Oscillating Tableaux, Sp x Sq -modules, and Robinson-Schensted-Knuth correspondence
• THE PRODUCT REPLACEMENT ALGORITHM AND KAZHDAN'S PROPERTY (T)
• TESTING COMMUTATIVITY OF A GROUP AND THE POWER OF RANDOMIZATION
• On tilings by ribbon tetrominoes Roman Muchnik, Igor Pak
• LONG CYCLES IN ABC-PERMUTATIONS IGOR PAK* AND AMANDA REDLICH*
• TILE INVARIANTS: NEW HORIZONS Igor Pak
• ON MIXING OF CERTAIN RANDOM WALKS, CUTOFF PHENOMENON AND SHARP
• THE PRODUCT REPLACEMENT GRAPH ON GENERATING TRIPLES OF PERMUTATIONS
• ON SAMPLING INTEGER POINTS IN POLYHEDRA Igor Pak
• Lifting Markov Chains to Speed up Mixing Fang Chen L6szl6 Lo&z *
• ---. ^9, . 6(300) 2 . 0-1-2 80
• TESTING COMMUTATIVITY OF A GROUP AND THE POWER OF RANDOMIZATION
• ON SAMPLING INTEGER POINTS IN POLYHEDRA Department of Mathematics,
• The product replacement algorithm is polynomial Department of Mathematics
• GROUPS OF OSCILLATING INTERMEDIATE GROWTH MARTIN KASSABOV AND IGOR PAK
• TESTING COMMUTATIVITY OF A GROUP AND THE POWER OF RANDOMIZATION
• FPSAC 2010, San Francisco, USA DMTCS proc. (subm.), by the authors, 112 Weighted branching formulas for the hook
• TRIANGULATIONS OF CAYLEY AND TUTTE POLYTOPES MATJAZ KONVALINKA
• Noncommutative Lagrange Theorem and Inversion Polynomials Igor Pak, Alexander Postnikov, Vladimir Retakh
• TILING SIMPLY CONNECTED REGIONS WITH RECTANGLES IGOR PAK AND JED YANG
• PERCOLATION ON GRIGORCHUK Roman Muchnik and Igor Pak
• GENERALIZED LOOP-ERASED RANDOM WALKS AND APPROXIMATE REACHABILITY
• On growth of Grigorchuk groups Roman Muchnik, Igor Pak
• GROUPS OF OSCILLATING INTERMEDIATE GROWTH MARTIN KASSABOV # AND IGOR PAK +
• TESTING COMMUTATIVITY OF A GROUP AND THE POWER OF RANDOMIZATION
• THE WEIGHTED HOOK LENGTH FORMULA IONUT CIOCANFONTANINE # , MATJA Z KONVALINKA + , AND IGOR PAK #
• FPSAC 2010, San Francisco, USA DMTCS proc. (subm.), by the authors, 1--12 Weighted branching formulas for the hook
• THE WEIGHTED HOOK LENGTH FORMULA IONUT CIOCAN-FONTANINE, MATJAZ KONVALINKA, AND IGOR PAK