Counting tableaux with row and column bounds
type: Item
instance of: scholarly article
title: Counting tableaux with row and column bounds
zbMATH Open document ID: 0824.05060
DOI: 10.1016/0012-365X(94)00136-7
published in: Discrete Mathematics
publication date: 1995-07-13T00:00:00Z
review text: It is well known that the generating function for tableaux of a given skew shape with \(r\) rows where the parts in the \(i\)th row are bounded by some nondecreasing upper and lower bounds which depend on \(i\) can be written in the form of a determinant of size \(r\). We show that the generating function for tableaux of a given skew shape with \(r\) rows and \(c\) columns where the parts in the \(i\)th row are bounded by nondecreasing upper and lower bounds which depend on \(i\) and the parts in the \(j\)th column are bounded by nondecreasing upper and lower bounds which depend on \(j\) can also be given in determinantal form. The size of the determinant now is \(r+ 2c\). We also show that determinants can be obtained when the nondecreasingness is dropped. Subsequently, analogous results are derived for \((\alpha, \beta)\)-plane partitions.
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 773913
zbMATH Keywords: generating functions
zbMATH Keywords: nonintersecting lattice paths
zbMATH Keywords: plane partitions
zbMATH Keywords: tableaux
zbMATH Keywords: determinants
author: C. Krattenthaler
author: S. G. Mohanty
MaRDI profile type: Publication
cites work: Dominance method for plane partitions. IV: Enumeration of flagged skew tableaux
cites work: Binomial determinants, paths, and hook length formulae
cites work: Generating functions for plane partitions of a given shape
cites work: Q3947818
cites work: Q3903764
cites work: Flagged Schur functions, Schubert polynomials, and symmetrizing operators
description: scientific article; zbMATH DE number 773913