Row-convex tableaux and the combinatorics of initial terms
type: Item
instance of: scholarly article
title: Row-convex tableaux and the combinatorics of initial terms
zbMATH Open document ID: 0969.05067
DOI: 10.1016/S0012-365X(99)00274-5
author: B. D. Taylor
published in: Discrete Mathematics
publication date: 2001-10-03T00:00:00Z
review text: A row-convex shape is a generalization of a Young diagram in which the only restriction is a shape which has no gaps in any row. A straight tableau is similar to a standard tableau whose column strict condition has been relaxed in a specific way. Via an algorithmic content preserving bisection between straight and standard tableaux and the inverse of the bisection we obtain a basis for the Schur module associated with a row-convex shape. The initial terms under a diagonal term order are also described, and the set of biwords corresponding to these terms is shown to be dual-Knuth closed. A corollary to a theorem on sorted biwords and straight tableaux yields that the recording tableaux for biwords corresponding to initial terms are decomposable. To conclude the matrix for the natural action of bases for the Schur module associated with a row-convex shape is shown to be unitriangular.
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1453363
zbMATH Keywords: representations
zbMATH Keywords: generalized Young tableaux
zbMATH Keywords: supersymmetric algebra
zbMATH Keywords: row-convex shape
zbMATH Keywords: straight tableaux
reviewed by: Stephanie van Willigenburg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453363