You are on the first page of X.V. new website www.viennot.org
During the reconstruction the "old" website www.xavierviennot.org is still active,
together with the sub-websites (Part I and II) dedicated to the "The Art of Bijective Combinatorics" I am giving at IMSc, Chennai, India.
Part I: An introduction to enumerative, algebraic and bijective combinatorics (January-March 2016)
Part II: Commutations and heaps of pieces with interactions in physics,
mathematics and computer science (January-March 2017)
last update: 31 May 2018
A mirror image of this website is here at IMSc , the Institute of Maths Science at Chennai, India (last update 22 April 2018.
The Art of Bijective Combinatorics, Part III:
The cellular ansatz: bijective combinatorics and quadratic algebra
Robinson-Schensted-Knuth, Asymmetric Exclusion Process, Tilings, Alternating Sign Matrices ... under the same roof
The Institute of Mathematical Sciences (IMSc), Chennai, India (January-March 2018)
Monday and Thursday, 11h30-13h, video room, first class: 4th January
79th SLC (Séminaire Lotharingien de Combinatoire), Bertinoro, Italy, 11 September 2017
Maule: tilings, Young and Tamari lattices under the same roof
slides part I (pdf, 25 Mo) tilings, Young and Tamari lattices as maules
slides part II (pdf, 26 Mo) Tamari(v) as a maule + comments and references added after the talk
Same lectures is given at IMSc, Chennai, India in two video-recorded Maths seminars 19 and 26 February 2018
(slightly augmented) set of slides and video links are available on this page.
Growth diagrams, local rules and beyond
21st Ramanujan Symposium: National Conference on algebra and its applications,
Ramanujan Institute, University of Madras, Chennai, India, 28 February 2018
slides part I (pdf, 17 Mo)
slides part II (pdf, 15 Mo)
Robinson-Schensted-Knuth correspondence (RSK), Schützenberger "jeu de taquin", Littlewood-Richarson coefficients are very classical objects in the combinatorics of Young tableaux, Schur functions and representation theory. Description has been given by Fomin in terms of "growth diagrams" and operators satisfying the commutation rules of the Weyl-Heisenberg algebra. After a survey of Fomin's approach, I will make a slight shift by introducing an equivalent description with "local rules on edges", and show how such point of view can be extended to some other quadratic algebras.
Growth diagrams and edge local rules
GASCom 2018, Athens, Greece, 18 June 2018
slides preliminary version: (pdf, 33Mo) GT LaBRI, Bordeaux, June 1st 2018
paper (extended abstract, 10p. in Proceedings GASCom 2018)
Fomin growth diagrams for the Robinson-Schensted correspondence and for the jeu de taquin are some rules allowing the construction of the 4th Ferrers diagram once 3 Ferrers diagrams around an elementary cell are known.We propose here to replace these rules by some local rules on edges instead of local rules on vertices.
Fomin growth diagrams, edge local rules, Schützenberger jeu de taquin, RSK product of two words, duality of Young tableaux.