A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin
type: Item
instance of: scholarly article
title: A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin
zbMATH Open document ID: 0858.05005
published in: The Electronic Journal of Combinatorics
publication date: 1996-07-21T00:00:00Z
full work available at URL: https://eudml.org/doc/119051
full work available at URL: R14
review text: The author gives a bijective proof of the product formula for the principal specialization of super Schur functions (also called hook Schur functions) using the combinatorial description of super Schur functions in terms of certain tableaux due to Berele and Regev [cf. \textit{A. Berele} and \textit{A. Regev}, Hook Young diagrams with applications to combinatorics and representations of Lie superalgebras, Adv. Math. 44, 118-175 (1987; Zbl 0617.17002)]. His bijective proof is based on the Hillman-Grassl algorithm [cf. \textit{A. P. Hillman} and \textit{R. M. Grassl}, Reverse plane partitions and tableau hook numbers, J. Comb. Theory, Ser. A 21, 216-221 (1976; Zbl 0341.05008)] and a modified version of Schützenberger's jeu de taquin. He then explores the relationship between his modified jeu de taquin and a modified jeu de taquin by \textit{I. Goulden} and \textit{C. Green} [A new tableau representation for supersymmetric Schur functions, J. Algebra 170, No. 2, 687-703 (1994; Zbl 0840.20008)]. He defines a common extension and proves an invariance property for it, thus discovering that both modified jeu de taquins are, though different, equivalent.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 907653
zbMATH Keywords: plane partitions
zbMATH Keywords: hook-content formula
zbMATH Keywords: super Schur functions
zbMATH Keywords: hook Schur functions
zbMATH Keywords: tableaux
zbMATH Keywords: Hillman-Grassl algorithm
zbMATH Keywords: jeu de taquin
author: C. Krattenthaler
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 907653