(part 3) Algèbres d opérateurs et Physique combinatoire. Xavier Viennot CNRS, LaBRI, Bordeaux
|
|
|
- Alexis Lambert
- 5 years ago
- Views:
Transcription
1 Algèbres d opérateurs et Physique combinatoire (part 3) 12 Avril 2012 colloquium de l IMJ Institut mathématiques de Jussieu Xavier Viennot CNRS, LaBRI, Bordeaux
2 quadratic algebra operators data structures and orthogonal polynomials
3 Primitive operations for dictionnaries data structure: add or delete any elements, asking questions (with positive or negative answer)
4 number of choices for each primitive operations
5 (formal) orthogonal polynomials
6
7
8 combinatorial interpretation of the moments
9
10
11
12
13 continued fractions 1980 orthogonal polynomials P. Flajolet Lecture Note X.V. 1983
14 PASEP algebra DE = qed + E + D q-laguerre polynomials
15
16
17
18
19 q-analogue of Laguerre histories choices function q-laguerre : q 4
20
21 general PASEP
22
23 Askey-Wilson
24 relation with moments of Askey-Wilson polynomials Corteel, Williams, 2009 Corteel, Stanley, Stanton, Williams, 2010
25
26 The cellular Ansatz From quadratic algebra Q to combinatorial objects (Q-tableaux) and bijections
27 "The cellular Ansatz" Physics "normal ordering" UD = DU + Id Weyl-Heisenberg DE = qed + E + D PASEP quadratic algebra Q commutations rewriting rules planarisation combinatorial objects on a 2d lattice towers placements permutations tableaux alternatifs Q-tableaux ex: ASM, (alternating sign matrices) FPL(fully packed loops) tilings, 8-vertex planar automata bijections RSK representation by operators data structures "histories" orthogonal polynomials pairs of Tableaux Young permutations Laguerre histories Koszul algebras duality
28 The 8-vertex algebra (or XYZ - algebra) (or Z - algebra)
29
30
31
32
33
34 2
35 2 n(n-1)/2 A (2) n Elkies, Kuperberg, Larsen, Propp (1992)
36 random Aztec tilings
37
38
39 example: binomial determinant
40
41 Razumov - Stroganov (ex)- conjecture
42
43
44
45
46
47
48 FPL Fully packed loop configurations
49 The bijection AMS FPL
50 The 6-vertex model
51
52 FPL Fully Packed Loop configuration
53 random FPL
54 Razumov-Stroganov conjecture stationary probabilities Di Francesco, P. Zinn-Justin (2005)
55 Around the Razumov-Stroganov conjecture Philippe Di Francesco, Paul Zinn-Justin ( ) De Gier, Pyatov (2007) Knizhnik - Zamolodchikov equation qkz TSSCPP ASM
56 Di Francesco (2006)
57 ASM 1-, 2-, 3- enumeration A (x) n Colomo, Pronco, (2004) Hankel determinants (continuous) Hahn, Meixner-Pollaczek, (continuous) dual Hahn orthogonal polynomials Ismail, Lin, Roan (2004) XXZ spin chains and Askey-Wilson operator Schubert and Grothendick polynomials Lascoux, Schützenberger
58 Razumov - Stroganov (ex)- conjecture proof by : L. Cantini and A.Sportiello (March 2010) arxiv: [math.c0] completely combinatorial proof
59 "The cellular Ansatz" Physics "normal ordering" UD = DU + Id Weyl-Heisenberg DE = qed + E + D PASEP quadratic algebra Q commutations rewriting rules planarisation combinatorial objects on a 2d lattice towers placements permutations tableaux alternatifs Q-tableaux ex: ASM, (alternating sign matrices) FPL(fully packed loops) tilings, 8-vertex planar automata bijections RSK representation by operators data structures "histories" orthogonal polynomials pairs of Tableaux Young permutations Laguerre histories? Koszul algebras duality
60 more details, see the diaporamas: Cours XGV, Universidad de Talca «The Cellular Ansatz» (December January 2011) Combinatorics and interactions (with physics) (24h) also: 4 talks in India January-March 2012 or «Petite Ecole de Combinatoire» LaBRI, Fall 2011, Spring 2012 and 2 videos: Newton Institute 23 April /csm/csmw04/0423/viennot/ IMSc, Chennai, 1 March accessible from the websites: Recherche, cv, publications, exposés, diaporamas, livres, petite école, photos: voir ma page personnelle ici Vulgarisation scientifique voir la page de l'association Cont'Science
61 Ch 0 Introduction Ch 1 Ordinary generating function, the Catalan garden Ch1a (1/12/2010, 54 p.) Ch 1b (7/12/2010, 81 p.) Ch 1c (7/12/2010, 30 p.) algebraic complements in relation with physics Ch 2 Exponential generating functions, permutations Ch 2a (22/12/2010, 40 p.) Ch 2b (4/01/2010, 63 p.) Ch 2c (4/01/2010, 33 p.) Permutations: Laguerre histories Cours XGV Universidad de Talca (December January 2011) 24 h Combinatorics and interactions (with physics) «The Cellular Ansatz» Ch 3 Permutations and Young tableaux, the Robinson-Schensted correspondence (RSK) Ch 3a (6/01/2011, 117 p.) Ch 3b (6, 11/01/2011, 121 p.) RSK and operators Ch 4 Alternative tableaux and the PASEP (partially asymmetric exclusion process) Ch 4a (13/01/2011, 98p.) Ch 4b (13, 18/01/2011, 102 p.) alternative tableaux and the PASEP Ch 4c (18/01/2011, 81 p.) complements Ch 5 Combinatorial theory of orthogonal polynomials (20/01/2011, 110 p.) Ch 6 "jeu de taquin" for binary trees, Catalan tableaux and the TASEP Ch 6a (24/01/2011, 98 p.) Ch 6b (24/01/2011, 111 p.) alternative tableaux and increasing/alternative binary trees Ch 6c (24/01/2011, 21 p.) Catalan tableaux and the Loday-Ronco algebra Ch 7 The cellular Ansatz Ch 7a (25/01/2011, 117 p.) Ch 7b (25/01/2011, 49 p.) complements
62 U B A MERCI! D A B
63
The combinatorics of some exclusion model in physics
The combinatorics of some exclusion model in physics Orsay 5 April 2012 Xavier G. Viennot CNRS, Bordeaux, France The PASEP Partialy asymmetric exclusion process The Matrix Ansatz Derrida, Evans, Hakim,
Algebraic Combinatorics and interactions The cellular Ansatz. Chapter 3 Alternative tableaux and the PASEP algebra DE=ED+E+D (part II)
Algebraic Combinatorics and interactions The cellular Ansatz Chapter 3 Alternative tableaux and the PASEP algebra DE=ED+E+D (part II) (Partially ASymmetric Exclusion Process) IIT-Bombay January 23, 2013
A MARKOV CHAIN ON THE SYMMETRIC GROUP WHICH IS SCHUBERT POSITIVE?
A MARKOV CHAIN ON THE SYMMETRIC GROUP WHICH IS SCHUBERT POSITIVE? THOMAS LAM AND LAUREN WILLIAMS Abstract. We study a multivariate Markov chain on the symmetric group with remarkable enumerative properties.
arxiv: v2 [math.co] 18 May 2009
![arxiv: v2 [math.co] 18 May 2009](/thumbs/82/86046526.jpg "arxiv: v2 [math.co] 18 May 2009")
KEYS AND ALTERNATING SIGN MATRICES arxiv:0711.2150v2 [math.co] 18 May 2009 JEAN-CHRISTOPHE AVAL Abstract. In [12], Lascoux and Schützenberger introduced a notion of key associated to any Young tableau.
The toggle group, homomesy, and the Razumov-Stroganov correspondence
The toggle group, homomesy, and the Razumov-Stroganov correspondence Jessica Striker Department of Mathematics North Dakota State University Fargo, North Dakota, U.S.A. jessica.striker@ndsu.edu Submitted:
Fully Packed Loops Model: Integrability and Combinatorics. Plan
ully Packed Loops Model 1 Fully Packed Loops Model: Integrability and Combinatorics Moscow 05/04 P. Di Francesco, P. Zinn-Justin, Jean-Bernard Zuber, math.co/0311220 J. Jacobsen, P. Zinn-Justin, math-ph/0402008
Fully packed loop configurations: polynomiality and nested arches
Fully packed loop configurations: polynomiality and nested arches Florian Aigner Universität Wien, Fakultät für Mathematik Oskar-Morgenstern-Platz 1, 1090 Wien, Austria florian.aigner@univie.ac.at Submitted:
Hankel determinants, continued fractions, orthgonal polynomials, and hypergeometric series
Hankel determinants, continued fractions, orthgonal polynomials, and hypergeometric series Ira M. Gessel with Jiang Zeng and Guoce Xin LaBRI June 8, 2007 Continued fractions and Hankel determinants There
Random Tilings Workshop Schedule
Random Tilings Workshop Schedule Monday, February 18 10:15am Fillipo Colomo A third- order phase transition in random tilings 11:30am Bernard Nienhuis Solvable incommensurable random tilings 2:30pm Greta
The spectrum of an asymmetric annihilation process
The spectrum of an asymmetric annihilation process arxiv:1008.2134v1 [math.co] 12 Aug 2010 Arvind Ayyer 1 and Volker Strehl 2 1 Institut de Physique Théorique, C. E. A. Saclay, 91191 Gif-sur-Yvette Cedex,
Coxeter-Knuth Graphs and a signed Little Bijection
Coxeter-Knuth Graphs and a signed Little Bijection Sara Billey University of Washington http://www.math.washington.edu/ billey AMS-MAA Joint Meetings January 17, 2014 0-0 Outline Based on joint work with
Schur processes and dimer models
Schur processes and dimer models Jérémie Bouttier Based on joint works with Dan Betea, Cédric Boutillier, Guillaume Chapuy, Sylvie Corteel, Sanjay Ramassamy and Mirjana Vuletić Institut de Physique Théorique,
The Arctic Circle re-revisited
`Workshop on Combinatorial Physics' Cardiff, 17-19 December 2013 The Arctic Circle re-revisited Filippo Colomo INFN, Firenze Joint work with: Andrei Pronko (PDMI-Steklov, Saint-Petersbourg) Domino tiling
A Simple Proof of the Aztec Diamond Theorem
A Simple Proof of the Aztec Diamond Theorem Sen-Peng Eu Department of Applied Mathematics National University of Kaohsiung Kaohsiung 811, Taiwan, ROC speu@nuk.edu.tw Tung-Shan Fu Mathematics Faculty National
COUNTING WITH AB-BA=1
COUNTING WITH AB-BA=1 PHILIPPE FLAJOLET, ROCQUENCOURT & PAWEL BLASIAK, KRAKÓW COMBINATORIAL MODELS OF ANNIHILATION-CREATION ; IN PREP. (2010) 1 A. = + + B. = 2 Annihilation and Creation A = Annihilate
Tiling expression of minors
Institute for Mathematics and its Applications Minneapolis, MN Colloquium University of British Columbia, Vancourver February, 0 Outline Introduction to the Enumeration of Tilings. Electrical networks
Formal Power Series and Algebraic Combinatorics Séries Formelles et Combinatoire Algébrique San Diego, California 2006
Formal Power Series and Algebraic Combinatorics Séries Formelles et Combinatoire Algébrique San Diego, California 2006 Dual Graded Graphs and Fomin s r-correspondences associated to the Hopf Algebras of
INVERSION OF INTEGRAL SERIES ENUMERATING PLANAR TREES
Séminaire Lotharingien de Combinatoire 53 (2005), Article B53d INVERSION OF INTEGRAL SERIES ENUMERATING PLANAR TREES JEAN-LOUIS LODAY Abstract. We consider an integral series f(x, t) which depends on the
ON THE ASYMPTOTIC DISTRIBUTION OF PARAMETERS IN RANDOM WEIGHTED STAIRCASE TABLEAUX
ON THE ASYMPTOTIC DISTRIBUTION OF PARAMETERS IN RANDOM WEIGHTED STAIRCASE TABLEAUX PAWE L HITCZENKO AND AMANDA PARSHALL Abstract In this paper, we study staircase tableaux, a combinatorial object introduced
Pieri s Formula for Generalized Schur Polynomials
Formal Power Series and Algebraic Combinatorics Séries Formelles et Combinatoire Algébrique San Diego, California 2006 Pieri s Formula for Generalized Schur Polynomials Abstract. We define a generalization
Statistical Mechanics, Integrability and Combinatorics
Il Colle di Galileo RAPPORTI DI ATTIVITÀ/ACTIVITY REPORTS Statistical Mechanics, Integrability and Combinatorics Galileo Galilei Institute for Theoretical Physics, Arcetri, Florence May 11 July 3, 2015
Factorization of the Robinson-Schensted-Knuth Correspondence
Factorization of the Robinson-Schensted-Knuth Correspondence David P. Little September, 00 Abstract In [], a bijection between collections of reduced factorizations of elements of the symmetric group was
The many faces of alternating-sign matrices
The many faces of alternating-sign matrices James Propp Department of Mathematics University of Wisconsin Madison, Wisconsin, USA propp@math.wisc.edu August 15, 2002 Abstract I give a survey of different
Combinatorial proofs of addition formulas
Combinatorial proofs of addition formulas Xiang-Ke Chang Xing-Biao Hu LSEC, ICMSEC, Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing, China Hongchuan Lei College of Science
Higher Spin Alternating Sign Matrices
Higher Spin Alternating Sign Matrices Roger E. Behrend and Vincent A. Knight School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK behrendr@cardiff.ac.uk, knightva@cardiff.ac.uk Submitted: Aug
Gog and Magog Triangles
Gog and Magog Triangles Philippe Biane To cite this version: Philippe Biane. Gog and Magog Triangles. Computation and Combinatorics in Dynamics, Stochastics and Control- The Abel Symposium, Rosendal, Norway,
arxiv: v1 [math.co] 6 Jun 2014
![arxiv: v1 [math.co] 6 Jun 2014](/thumbs/95/124604362.jpg "arxiv: v1 [math.co] 6 Jun 2014")
WIELAND GYRATION FOR TRIANGULAR FULLY PACKED LOOP CONFIGURATIONS SABINE BEIL, ILSE FISCHER, AND PHILIPPE NADEAU arxiv:1406.1657v1 [math.co] 6 Jun 2014 Abstract. Triangular fully packed loop configurations
Six-vertex model partition functions and symmetric polynomials of type BC
Six-vertex model partition functions and symmetric polynomials of type BC Dan Betea LPMA (UPMC Paris 6), CNRS (Collaboration with Michael Wheeler, Paul Zinn-Justin) Iunius XXVI, MMXIV This message is proudly
Combinatorics of non-associative binary operations
Combinatorics of non-associative binary operations Jia Huang University of Nebraska at Kearney E-mail address: huangj2@unk.edu December 26, 2017 This is joint work with Nickolas Hein (Benedictine College),
Refined Cauchy/Littlewood identities and partition functions of the six-vertex model
Refined Cauchy/Littlewood identities and partition functions of the six-vertex model LPTHE (UPMC Paris 6), CNRS (Collaboration with Dan Betea and Paul Zinn-Justin) 6 June, 4 Disclaimer: the word Baxterize
COMBINATORICS OF THE TWO-SPECIES ASEP AND KOORNWINDER MOMENTS
COMBINATORICS OF THE TWO-SPECIES ASEP AND KOORNWINDER MOMENTS SYLVIE CORTEEL, OLYA MANDELSHTAM, AND LAUREN WILLIAMS Abstract. In previous work [CW10, CW11, CW13], the first and third authors introduced
MULTI-ORDERED POSETS. Lisa Bishop Department of Mathematics, Occidental College, Los Angeles, CA 90041, United States.
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A06 MULTI-ORDERED POSETS Lisa Bishop Department of Mathematics, Occidental College, Los Angeles, CA 90041, United States lbishop@oxy.edu
THE Q-SPECTRUM AND SPANNING TREES OF TENSOR PRODUCTS OF BIPARTITE GRAPHS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 125, Number 11, November 1997, Pages 3155 3161 S 0002-9939(9704049-5 THE Q-SPECTRUM AND SPANNING TREES OF TENSOR PRODUCTS OF BIPARTITE GRAPHS TIMOTHY
Finding parking when not commuting. Jon McCammond U.C. Santa Barbara
Finding parking when not commuting PSfrag replacements 7 8 1 2 6 3 5 {{1, 4, 5}, {2, 3}, {6, 8}, {7}} 4 Jon McCammond U.C. Santa Barbara 1 A common structure The goal of this talk will be to introduce
The dilute Temperley-Lieb O(n = 1) loop model on a semi infinite strip: the ground state
The dilute Temperley-Lieb O(n = 1) loop model on a semi infinite strip: the ground state arxiv:1411.7020v1 [math-ph] 25 Nov 2014 A. Garbali 1 and B. Nienhuis 2 1 LPTHE, CNRS UMR 7589, Université Pierre
2 J. ZENG THEOREM 1. In the ring of formal power series of x the following identities hold : (1:4) 1 + X n1 =1 S q [n; ]a x n = 1 ax? aq x 2 b x? +1 x
![2 J. ZENG THEOREM 1. In the ring of formal power series of x the following identities hold : (1:4) 1 + X n1 =1 S q [n; ]a x n = 1 ax? aq x 2 b x? +1 x](/thumbs/81/83785321.jpg "2 J. ZENG THEOREM 1. In the ring of formal power series of x the following identities hold : (1:4) 1 + X n1 =1 S q [n; ]a x n = 1 ax? aq x 2 b x? +1 x")
THE q-stirling NUMBERS CONTINUED FRACTIONS AND THE q-charlier AND q-laguerre POLYNOMIALS By Jiang ZENG Abstract. We give a simple proof of the continued fraction expansions of the ordinary generating functions
Coxeter-Knuth Classes and a Signed Little Bijection
Coxeter-Knuth Classes and a Signed Little Bijection Sara Billey University of Washington Based on joint work with: Zachary Hamaker, Austin Roberts, and Benjamin Young. UC Berkeley, February, 04 Outline
Proof of a generalization of Aztec diamond theorem
Proof of a generalization of Aztec diamond theorem Institute for Mathematics and its Applications University of Minnesota Minneapolis, MN 55455 December 5, 2014 Aztec Diamond Theorem Definition The Aztec
From alternating sign matrices to Painlevé VI
From alternating sign matrices to Painlevé VI Hjalmar Rosengren Chalmers University of Technology and University of Gothenburg Nagoya, July 31, 2012 Hjalmar Rosengren (Chalmers University) Nagoya, July
Wieland drift for triangular fully packed loop configurations
Wieland drift for triangular fully packed loop configurations Sabine Beil Ilse Fischer Fakultät für Mathematik Universität Wien Wien, Austria {sabine.beil,ilse.fischer}@univie.ac.at Philippe Nadeau Institut
The half-plactic monoïd
de 37 The half-plactic monoïd Nathann Cohen and Florent Hivert LRI / Université Paris Sud / CNRS Fevrier 205 2 de 37 Outline Background: plactic like monoïds Schensted s algorithm and the plactic monoïd
Standard Young Tableaux Old and New
Standard Young Tableaux Old and New Ron Adin and Yuval Roichman Department of Mathematics Bar-Ilan University Workshop on Group Theory in Memory of David Chillag Technion, Haifa, Oct. 14 1 2 4 3 5 7 6
Algebras, Operads, Combinads
Algebras, Operads, Combinads Jean-Louis Loday IRMA (Cnrs) et Institut de Mathématique Zinbiel, Strasbourg HOGT Lille, 23 mars 2012 Plan of the talk I. Types of algebras, types of operads Plan of the talk
A Course in Combinatorics
A Course in Combinatorics J. H. van Lint Technical Universüy of Eindhoven and R. M. Wilson California Institute of Technology H CAMBRIDGE UNIVERSITY PRESS CONTENTS Preface xi 1. Graphs 1 Terminology of
q-alg/ v2 15 Sep 1997
DOMINO TABLEAUX, SCH UTZENBERGER INVOLUTION, AND THE SYMMETRIC GROUP ACTION ARKADY BERENSTEIN Department of Mathematics, Cornell University Ithaca, NY 14853, U.S.A. q-alg/9709010 v 15 Sep 1997 ANATOL N.
Finding parking when not commuting. Jon McCammond U.C. Santa Barbara
Finding parking when not commuting 7 6 8 1 2 3 5 4 {{1,4,5}, {2,3}, {6,8}, {7}} Jon McCammond U.C. Santa Barbara 1 A common structure The main goal of this talk will be to introduce you to a mathematical
A note on quantum products of Schubert classes in a Grassmannian
J Algebr Comb (2007) 25:349 356 DOI 10.1007/s10801-006-0040-5 A note on quantum products of Schubert classes in a Grassmannian Dave Anderson Received: 22 August 2006 / Accepted: 14 September 2006 / Published
arxiv:math.co/ v2 3 Oct 2003
Loops, matchings and alternating-sign matrices arxiv:math.co/0211285 v2 3 Oct 2003 Jan de Gier Department of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
Quantum Knizhnik Zamolodchikov equation, generalized Razumov Stroganov sum rules and extended Joseph polynomials
SPhT-T05/130 arxiv:math-ph/0508059v3 7 Mar 2006 Quantum Knizhnik Zamolodchikov equation, generalized Razumov Stroganov sum rules and extended Joseph polynomials P. Di Francesco # and P. Zinn-Justin We
DIFFERENTIAL POSETS SIMON RUBINSTEIN-SALZEDO
DIFFERENTIAL POSETS SIMON RUBINSTEIN-SALZEDO Abstract. In this paper, we give a sampling of the theory of differential posets, including various topics that excited me. Most of the material is taken from
arxiv: v2 [math.rt] 28 Aug 2018
![arxiv: v2 [math.rt] 28 Aug 2018](/thumbs/84/90692776.jpg "arxiv: v2 [math.rt] 28 Aug 2018")
arxiv:1808.08679v2 [math.rt] 28 Aug 2018 Tableau Correspondences and Representation Theory DIGJOY PAUL AND AMRITANSHU PRASAD The Institute of Mathematical Sciences (HBNI) Chennai ARGHYA SADHUKHAN University
PUBLICATIONS SYLVIE CORTEEL
PUBLICATIONS SYLVIE CORTEEL Corteel, Sylvie; Williams, Lauren, Macdonald-Koornwinder moments and the two-species exclusion process, Selecta Mathematicae, Accepted 2017. Corteel, Sylvie; Mandelshtam, Olya;
Jessica Striker. November 10, 2015
Resonance in dynamical algebraic combinatorics Jessica Striker joint work with Kevin Dilks (NDSU) and Oliver Pechenik (UIUC) North Dakota State University November 10, 2015 J. Striker (NDSU) Resonance
Cluster Variables and Perfect Matchings of Subgraphs of the dp 3 Lattice
Cluster Variables and Perfect Matchings of Subgraphs of the dp Lattice Sicong Zhang October 8, 0 Abstract We give a combinatorial intepretation of cluster variables of a specific cluster algebra under
Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order Arvind Ayyer (Bangalore) Roger E. Behrend (Cardiff) Ilse Fischer (Vienna) 1 Outline Introduction: ASMs and DASASMs
The dilute Temperley-Lieb O(n = 1) loop model on a semi infinite strip: the sum rule
The dilute Temperley-Lieb O(n = 1) loop model on a semi infinite strip: the sum rule arxiv:1411.7160v1 [math-ph] 26 Nov 2014 A. Garbali 1 and B. Nienhuis 2 1 LPTHE, CNRS UMR 7589, Université Pierre et
Enumerative Combinatorics with Fillings of Polyominoes
Enumerative Combinatorics with Fillings of Polyominoes Catherine Yan Texas A&M University Tulane, March 205 Tulane, March 205 2 Outline. Symmetry of the longest chains Subsequences in permutations and
Cylindric Young Tableaux and their Properties
Cylindric Young Tableaux and their Properties Eric Neyman (Montgomery Blair High School) Mentor: Darij Grinberg (MIT) Fourth Annual MIT PRIMES Conference May 17, 2014 1 / 17 Introduction Young tableaux
Sergey Fomin* and. Minneapolis, MN We consider the partial order on partitions of integers dened by removal of
Rim Hook Lattices Sergey Fomin* Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139 Theory of Algorithms Laboratory St. Petersburg Institute of Informatics Russian Academy
The long way home. Orbits of plane partitions. Oliver Pechenik. University of Michigan. UM Undergraduate Math Club October 2017
Taking the long way home Orbits of plane partitions University of Michigan UM Undergraduate Math Club October 2017 Mostly based on joint work with Kevin Dilks and Jessica Striker (NDSU) motion of partitions
Dynamical algebraic combinatorics
Dynamical algebraic combinatorics organized by James Propp, Tom Roby, Jessica Striker, and Nathan Williams Workshop Summary Topics of the Workshop This workshop centered around dynamical systems arising
arxiv:math-ph/ v2 22 Dec 2004
Square ice, alternating sign matrices, and classical orthogonal polynomials arxiv:math-ph/0411076v2 22 Dec 2004 F. Colomo and A. G. Pronko 1 I..F.., Sezione di Firenze, and Dipartimento di Fisica, Università
Proofs & Confirmations The story of the alternating sign matrix conjecture
Proofs & Confirmations The story of the alternating sign matrix conjecture David M. Bressoud Macalester College University of Nebraska Omaha, NE These slides are available at www.macalester.edu/~bressoud/talks
Boolean Product Polynomials and the Resonance Arrangement
Boolean Product Polynomials and the Resonance Arrangement Sara Billey University of Washington Based on joint work with: Lou Billera and Vasu Tewari FPSAC July 17, 2018 Outline Symmetric Polynomials Schur
Domino tilings with barriers. In memory of Gian-Carlo Rota
Domino tilings with barriers In memory of Gian-Carlo Rota James Propp Richard Stanley University of Wisconsin, Madison, WI 53706 Massachusetts Institute of Technology, Cambridge, MA 02139 In this paper,
arxiv:math/ v2 [math.co] 15 Jan 2004
![arxiv:math/ v2 [math.co] 15 Jan 2004](/thumbs/93/112717454.jpg "arxiv:math/ v2 [math.co] 15 Jan 2004")
The Algebra of Binary Search Trees F. Hivert a,1, J.-C. Novelli b,1, and J.-Y. Thibon b,1 arxiv:math/0401089v2 [math.co] 15 Jan 2004 a Laboratoire Franco-Russe de Mathématiques, Independent University
A BIJECTION BETWEEN WELL-LABELLED POSITIVE PATHS AND MATCHINGS
Séminaire Lotharingien de Combinatoire 63 (0), Article B63e A BJECTON BETWEEN WELL-LABELLED POSTVE PATHS AND MATCHNGS OLVER BERNARD, BERTRAND DUPLANTER, AND PHLPPE NADEAU Abstract. A well-labelled positive
Ira M. Gessel Department of Mathematics, Brandeis University, P.O. Box 9110, Waltham, MA Revised September 30, 1988
GENERALIZED ROOK POLYNOMIALS AND ORTHOGONAL POLYNOMIALS Ira M. Gessel Department of Mathematics, Brandeis University, P.O. Box 9110, Waltham, MA 02254-9110 Revised September 30, 1988 Abstract. We consider
Reduced words and a formula of Macdonald
Reduced words and a formula of Macdonald Sara Billey University of Washington Based on joint work with: Alexander Holroyd and Benjamin Young preprint arxiv:70.096 Graduate Student Combinatorics Conference
FORMULAE FOR ASKEY-WILSON MOMENTS AND ENUMERATION OF STAIRCASE TABLEAUX
FORMULAE FOR ASKEY-WILSON MOMENTS AND ENUMERATION OF STAIRCASE TABLEAUX S. CORTEEL, R. STANLEY, D. STANTON, AND L. WILLIAMS Abstract. We explain how the moments of the (weight function of the) Askey Wilson
arxiv: v1 [math.ag] 11 Nov 2009
![arxiv: v1 [math.ag] 11 Nov 2009](/thumbs/80/81659958.jpg "arxiv: v1 [math.ag] 11 Nov 2009")
REALITY AND TRANSVERSALITY FOR SCHUBERT CALCULUS IN OG(n, 2n+1) arxiv:0911.2039v1 [math.ag] 11 Nov 2009 KEVIN PURBHOO Abstract. We prove an analogue of the Mukhin-Tarasov-Varchenko theorem (formerly the
q xk y n k. , provided k < n. (This does not hold for k n.) Give a combinatorial proof of this recurrence by means of a bijective transformation.
Math 880 Alternative Challenge Problems Fall 2016 A1. Given, n 1, show that: m1 m 2 m = ( ) n+ 1 2 1, where the sum ranges over all positive integer solutions (m 1,..., m ) of m 1 + + m = n. Give both
Proofs of two conjectures of Kenyon and Wilson on Dyck tilings
FPSAC 202, Nagoya, Japan DMTCS proc. AR, 202, 36 372 Proofs of two conjectures of Kenyon and Wilson on Dyck tilings Jang Soo Kim School of Mathematics, University of Minnesota, USA. Abstract. Recently,
Resonance in orbits of plane partitions and increasing tableaux. Jessica Striker North Dakota State University
Resonance in orbits of plane partitions and increasing tableaux Jessica Striker North Dakota State University joint work with Kevin Dilks (NDSU) and Oliver Pechenik (UIUC) February 19, 2016 J. Striker
Tetrahedron equation and matrix product method
Tetrahedron equation and matrix product method Atsuo Kuniba (Univ. Tokyo) Joint work with S. Maruyama and M. Okado Reference Multispecies totally asymmetric zero range process I, II Journal of Integrable
Combinatorial Structures
Combinatorial Structures Contents 1 Permutations 1 Partitions.1 Ferrers diagrams....................................... Skew diagrams........................................ Dominance order......................................
Enumerative Combinatorics with Fillings of Polyominoes
Enumerative Combinatorics with Fillings of Polyominoes Catherine Yan Texas A&M Univesrity GSU, October, 204 2 Outline. Symmetry of the longest chains Subsequences in permutations and words Crossings and
Combinatorics of the Del-Pezzo 3 Quiver: Aztec Dragons, Castles, and Beyond
Combinatorics of the Del-Pezzo Quiver: Aztec Dragons, Castles, and Beyond Tri Lai (IMA) and Gregg Musiker (University of Minnesota) AMS Special Session on Integrable Combinatorics March, 0 http//math.umn.edu/
A zoo of Hopf algebras
Non-Commutative Symmetric Functions I: A zoo of Hopf algebras Mike Zabrocki York University Joint work with Nantel Bergeron, Anouk Bergeron-Brlek, Emmanurel Briand, Christophe Hohlweg, Christophe Reutenauer,
Dunkl operators, special functions and harmonic analysis. Schedule (as of August 8)
Dunkl operators, special functions and harmonic analysis Paderborn University August 8-12, 2016 Schedule (as of August 8) Monday, August 8 8:30 9:30 Registration (room O1.224) 9:30 9:50 Opening (Lecture
Poset and Polytope Perspectives On Alternating Sign Matrices
Poset and Polytope Perspectives On Alternating Sign Matrices A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Jessica Palencia Striker IN PARTIAL FULFILLMENT
EQUIDISTRIBUTION AND SIGN-BALANCE ON 321-AVOIDING PERMUTATIONS
Séminaire Lotharingien de Combinatoire 51 (2004), Article B51d EQUIDISTRIBUTION AND SIGN-BALANCE ON 321-AVOIDING PERMUTATIONS RON M. ADIN AND YUVAL ROICHMAN Abstract. Let T n be the set of 321-avoiding
The Automorphism Group of the Fibonacci Poset: A Not Too Difficult Problem of Stanley from 1988
Journal of Algebraic Combinatorics, 19, 197 204, 2004 c 2004 Kluwer Academic Publishers. Manufactured in The Netherlands. The Automorphism Group of the Fibonacci Poset: A Not Too Difficult Problem of Stanley
Linear equivalence and identical Young tableau bijections for the conjugation symmetry of Littlewood-Richardson coefficients
Linear equivalence and identical Young tableau bijections for the conjugation symmetry of Littlewood-Richardson coefficients O. Azenhas, A. Conflitti, R. Mamede CMUC Centre for Mathematics, University
GENERALIZATION OF THE SIGN REVERSING INVOLUTION ON THE SPECIAL RIM HOOK TABLEAUX. Jaejin Lee
Korean J. Math. 8 (00), No., pp. 89 98 GENERALIZATION OF THE SIGN REVERSING INVOLUTION ON THE SPECIAL RIM HOOK TABLEAUX Jaejin Lee Abstract. Eğecioğlu and Remmel [] gave a combinatorial interpretation
A polynomial realization of the Hopf algebra of uniform block permutations.
FPSAC 202, Nagoya, Japan DMTCS proc AR, 202, 93 204 A polynomial realization of the Hopf algebra of uniform block permutations Rémi Maurice Institut Gaspard Monge, Université Paris-Est Marne-la-Vallée,
Around the Razumov Stroganov conjecture: proof of a multi-parameter sum rule
SPhT-T04/33 Around the Razumov Stroganov conjecture: proof of a multi-parameter sum rule P. Di Francesco # and P. Zinn-Justin We prove that the sum of entries of the suitably normalized groundstate vector
SHIFTED K-THEORETIC POIRIER-REUTENAUER BIALGEBRA
SHIFTED K-THEORETIC POIRIER-REUTENAUER BIALGEBRA ADAM KEILTHY, REBECCA PATRIAS, LILLIAN WEBSTER, YINUO ZHANG, SHUQI ZHOU Abstract We use shifted K-theoretic jeu de taquin to show that the weak K-Knuth
Enumerating rc-invariant Permutations with No Long Decreasing Subsequences
Enumerating rc-invariant Permutations with No Long Decreasing Subsequences Eric S. Egge Department of Mathematics Carleton College Northfield, MN 55057 USA eegge@carleton.edu Abstract We use the Robinson-Schensted-Knuth
CV of Dr. Takeo Kojima
CV of Dr. Takeo Kojima Name: Takeo Kojima Affiliation: Position: Professor Date Prepared: May 30, 2017 Day and Place of Birth: March 22, 1969, Japan Education March 1992 : B.S. Kyoto University, School
Tableau sequences, open diagrams, and Baxter families
Tableau sequences, open diagrams, and Baxter families Sophie Burrill a, Julien Courtiel a, Eric Fusy b, Stephen Melczer c, Marni Mishna a, a Department of Mathematics, Simon Fraser University, Burnaby,
Sergey Fomin* Theory of Algorithms Laboratory Institute of Informatics, Russian Academy of Sciences St.Petersburg , Russia
Sergey Fomin* Theory of Algorithms Laboratory Institute of Informatics, Russian Academy of Sciences St.Petersburg 199178, Russia and Dennis Stanton** School of Mathematics University of Minnesota Minneapolis,
arxiv:math/ v1 [math.co] 10 Nov 1998
![arxiv:math/ v1 [math.co] 10 Nov 1998](/thumbs/82/85857467.jpg "arxiv:math/ v1 [math.co] 10 Nov 1998")
A self-dual poset on objects counted by the Catalan numbers arxiv:math/9811067v1 [math.co] 10 Nov 1998 Miklós Bóna School of Mathematics Institute for Advanced Study Princeton, NJ 08540 April 11, 2017
arxiv: v1 [math.co] 6 Apr 2007
![arxiv: v1 [math.co] 6 Apr 2007](/thumbs/81/83850330.jpg "arxiv: v1 [math.co] 6 Apr 2007")
AN S -SYMMETRIC LITTLEWOOD-RICHARDSON RULE HUGH THOMAS AND ALEXANDER YONG arxiv:070.087v [math.co] 6 Apr 2007. INTRODUCTION Fix Young shapes λ, µ, ν Λ := l k. Viewing the Littlewood-Richardson coefficients
Enumeration of domino tilings of a double Aztec rectangle
Enumeration of domino tilings of a double Aztec rectangle University of Nebraska Lincoln Lincoln, NE 68505 AMS Fall Central Sectional Meeting University of St. Thomas Minneapolis, MN, October 30, 2015
Combinatorics for algebraic geometers
Combinatorics for algebraic geometers Calculations in enumerative geometry Maria Monks March 17, 214 Motivation Enumerative geometry In the late 18 s, Hermann Schubert investigated problems in what is
THE THEORY OF HEAPS AND THE CARTIER FOATA MONOID. C. Krattenthaler
THE THEORY OF HEAPS AND THE CARTIER FOATA MONOID C Krattenthaler Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Vienna, Austria WWW: http://wwwmatunivieacat/~kratt Abstract We present
A Pieri rule for key polynomials
Séminaire Lotharingien de Combinatoire 80B (2018) Article #78, 12 pp. Proceedings of the 30 th Conference on Formal Power Series and Algebraic Combinatorics (Hanover) A Pieri rule for key polynomials Sami
J. Stat. Mech. (2005) P01006
Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Jan de Gier 1 and Bernard Nienhuis 2 1 Department of Mathematics and Statistics, The University of Melbourne, VIC 3010,
arxiv: v1 [math.rt] 5 Aug 2016
![arxiv: v1 [math.rt] 5 Aug 2016](/thumbs/75/71797850.jpg "arxiv: v1 [math.rt] 5 Aug 2016")
AN ALGEBRAIC FORMULA FOR THE KOSTKA-FOULKES POLYNOMIALS arxiv:1608.01775v1 [math.rt] 5 Aug 2016 TIMOTHEE W. BRYAN, NAIHUAN JING Abstract. An algebraic formula for the Kostka-Foukles polynomials is given