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• W2158525989 abstract "Abstract Greene's Theorem relating chain and antichain families with maximal cardinalities in a poset (partially ordered set) was motivated by the Robinson-Schensted correspondence. This correspondence is a bijection between permutations and pairs (P, Q) of standard Young tableaux having the same shape. This bijection originated in the representation theory of the symmetric group. The underlying combinatorics is very deep and also takes roots in the theory of symmetric functions and algebraic geometry. The purpose of this talk is threefold. First we give a brief summary of the principal combinatorial properties of the Robinson-Schensted correspondence, especially those having an order-theoretical flavor. Second we shed some light on its relationship with poset theory and Greene's Theorem. The third purpose of this talk is to solve the following open problem : give an interpretation of the value located in the (i, j) cell of the Young tableaux P and Q. This “local” characterization of the correspondence is completely symmetric in rows and columns and requires the concept of grids and extendable grids. These last results can be extended to arbitrary posets. Complete proofs will be given elsewhere. Resume Le theoreme de Greene sur les cardinaux maximaux des families de chaines et d'antichaines extraites d'un ensemble (partiellement) ordonne a son origine dans la correspondance de Robinson-Schensted. Cette correspondance est une bijection entre les permutations et les paires (P, Q) de tableaux standards de Young de měme forme. Cette bijection provient en fait de la theorie des representations du groupe symetrique. La combinatoire sous-jacente est fort riche et prend egalement racine dans la theorie des fonctions symetriques et en geometrie algebrique. Le but de cet expose est triple. D'abord nous donnons un bref apercu des proprietes combinatoires les plus classiques de cette correspondance, notamment celles en relation avec la methodologie des ensembles ordonnes. Le deuxieme but de cet expose est de faire sentir a un public motive par les ensembles ordonnes l'interet de mieux connaitre cette merveilleuse correspondance. Enfin une troisieme partie est consacree a la resolution d'un probleme ouvert : dormer une interpretation symetrique en lignes et colonnes de la valeur situee dans la case (i, j) des tableaux de Young P et Q. Cette definition “locale” de la correspondance de Robinson-Schensted utilise les nouveaux concepts de grille et de grille prolongeable. Ces dernieres idees peuvent ětre etendues aux ensembles ordonnes quelconques. Les preuves completes de ces nouveaux resultants seront donnees ailleurs." @default.
• W2158525989 created "2016-06-24" @default.
• W2158525989 creator A5034846169 @default.
• W2158525989 date "1984-01-01" @default.
• W2158525989 modified "2023-09-23" @default.
• W2158525989 title "Chain and Antichain Families Grids and Young Tableaux" @default.
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• W2158525989 doi "https://doi.org/10.1016/s0304-0208(08)73835-0" @default.
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