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SUMMARY:String of columns rewriting and plactic-like monoids
DTSTART;VALUE=DATE-TIME:20200514T120000Z
DTEND;VALUE=DATE-TIME:20200514T130000Z
DTSTAMP;VALUE=DATE-TIME:20200526T184500Z
UID:indico-event-5814@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nohra HAGE\nLascoux and Schützenberger introduced t
he structure of plactic monoids after the works of Schensted and Knuth on
the combinatorial study of Young tableaux. Using his jeu de taquin\, Schü
tzenberger gave the first correct proof of the Littelwood-Richardsonrule.
This rule describes in a combinatorial way the multiplicity of a Schur pol
ynomial in\na product of Schur polynomials. Recently\, similar classes of
monoids such as hypoplactic\, Chinese\, Sylvester and patience sorting m
onoids are also introduced and have found several applications on algebrai
c combinatorics and representation theory.\n\n \n\nIn this talk\, we defi
ne plactic-like monoids using the notions of string of columns constructed
by insertion algorithms. We also introduce the notions of string data str
uctures and morphism of string data structures and we explain how such a m
orphism can transfer combinatorial properties from a string data structure
to another one\, using sliding\nalgorithms and string of columns rewritin
g. Finally\, we relate the string data structures of skew\, Young and quas
i-ribbon tableaux. In particular\, we describe Schützenberger's jeu de t
aquin as a string of columns rewriting\, showing that it is a morphism bet
ween the string data structures of skew and Young tableaux\, using rewriti
ng properties of the corresponding string of columns rewriting.\nhttps://i
ndico.math.cnrs.fr/event/5814/
LOCATION:112 virtuel (bât. Braconnier)
URL:https://indico.math.cnrs.fr/event/5814/
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