Trapezoidal chains and antichains
type: Item
instance of: scholarly article
title: Trapezoidal chains and antichains
zbMATH Open document ID: 0641.06001
DOI: 10.1016/S0195-6698(86)80009-9
author: John R. Stembridge
published in: European Journal of Combinatorics
publication date: 1986-01-01T00:00:00Z
review text: Further common properties of the partially ordered sets \(R(m,n)=\{(i,j)\in {\mathbb{Z}}^ 2:\) \(1\leq i\leq m\), \(1\leq j\leq n\}\) (a rectangle) and \(T(m,n)=\{(i,j)\in {\mathbb{Z}}^ 2:\) \(1\leq i\leq m\), \(i\leq j\leq m+n-i\}\) (a trapezoid) are established. Weights are attached to the antichains of R(m,n) and T(m,n) in such a way that the sum of the weights of the antichains in R(m,n) and T(m,n) are the same. A proof is given which exploits connections among antichains in T(m,n), the theory of Schur functions, and self-complementary tableaux. A bijection is given between the antichains of R(m,n) and T(m,n) which uses jeu de taquin. Similar weights, theorem, and bijections are also given for the multichains of R(m,n) and T(m,n).
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4043900
zbMATH Keywords: rectangle
zbMATH Keywords: trapezoid
zbMATH Keywords: antichains
zbMATH Keywords: weights
zbMATH Keywords: Schur functions
zbMATH Keywords: self- complementary tableaux
zbMATH Keywords: jeu de taquin
zbMATH Keywords: multichains
MaRDI profile type: Publication
cites work: Q3947818
cites work: Shifted Plane Partitions of Trapezoidal Shape
cites work: La correspondance de Robinson
cites work: Combinatorial reciprocity theorems
cites work: On the number of reduced decompositions of elements of Coxeter groups
cites work: Symmetries of plane partitions
description: scientific article; zbMATH DE number 4043900