Composition matrices, \((2+2)\)-free posets and their specializations
type: Item
instance of: scholarly article
title: Composition matrices, \((2+2)\)-free posets and their specializations
zbMATH Open document ID: 1290.05021
author: Mark Dukes
author: Vít Jelínek
author: Martina Kubitzke
published in: The Electronic Journal of Combinatorics
publication date: 2011-06-01T00:00:00Z
full work available at URL: v18i1p44.html
review text: Summary: In this paper we present a bijection between composition matrices and \((2 + 2)\)-free posets. This bijection maps partition matrices to factorial posets, and induces a bijection from upper triangular matrices with non-negative entries having no rows or columns of zeros to unlabeled \((2 + 2)\)-free posets. Chains in a \((2 + 2)\)-free poset are shown to correspond to entries in the associated composition matrix whose hooks satisfy a simple condition. It is shown that the action of taking the dual of a poset corresponds to reflecting the associated composition matrix in its anti-diagonal. We further characterize posets which are both \((2 + 2)\)- and \((3 + 1)\)-free by certain properties of their associated composition matrices.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 5902974
zbMATH Keywords: \((2+2)\)-free poset
zbMATH Keywords: dual poset
zbMATH Keywords: bijection, interval orders
zbMATH Keywords: composition matrix
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5902974