Tableau algorithms defined naturally for pictures
type: Item
instance of: scholarly article
title: Tableau algorithms defined naturally for pictures
zbMATH Open document ID: 0863.05080
DOI: 10.1016/S0012-365X(96)83022-6
author: Marc van Leeuwen
published in: Discrete Mathematics
publication date: 1996-10-14T00:00:00Z
review text: Given a skew tableau \(\chi\), we consider two partial orders: \((\chi, \nwarrow)\) in which there is increase from left to right and down columns and \((\chi, \swarrow)\) in which there is increase from left to right and up columns. Given a bijection between the positions in two skew tableaux, \(f:\chi \to\psi\), \(f\) is a picture if \(f(\chi, \nwarrow)\) is consistent with \((\psi, \swarrow)\) and \(f^{-1} (\psi, \nwarrow)\) is consistent with \((\chi, \swarrow) \). The Littlewood-Richardson rule can be stated in terms of pictures: \(c^\lambda_{\mu\nu}\) is the cardinality of the set of pictures from \(\lambda \backslash \mu\) to \(\nu\). Schützenberger's concept of glissement has a natural extension to pictures in which the glissement is applied to either the domain or the range. The author proves that these two forms of glissement commute, and this in turn simplifies the proofs of the main properties of glissement.
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 935387
zbMATH Keywords: skew tableau
zbMATH Keywords: picture
zbMATH Keywords: Littlewood-Richardson rule
zbMATH Keywords: glissement
reviewed by: David M. Bressoud
MaRDI profile type: Publication
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full work available at URL: s0012-365x(96)83022-6
OpenAlex ID: W2160916325
description: scientific article; zbMATH DE number 935387