A combinatorial property for semigroups of matrices.
type: Item
instance of: scholarly article
title: A combinatorial property for semigroups of matrices.
zbMATH Open document ID: 1037.20063
author: Elton Pasku
author: Flavio D'Alessandro
published in: Semigroup Forum
publication date: 2003-08-31T00:00:00Z
review text: A semigroup \(S\) has the weak permutation property if there exists some integer \(k\geq 2\) such that for any sequence \(s_1,s_2,\dots,s_k\) of elements of \(S\), there are distinct permutations \(\sigma\) and \(\tau\) of the set \(\{1,2,\dots,k\}\) such that \(s_{\sigma(1)}s_{\sigma(2)}\cdots s_{\sigma(k)}=s_{\tau(1)}s_{\tau(2)}\cdots s_{\tau(k)}\). In this article, the authors study the semigroups of matrices over a commutative semiring, proving that a semigroup of matrices \(S\) over a tropical semiring has the weak permutation property and that if \(S\) is finitely generated then the growth function of \(S\) is polynomially upper bounded. They also find an application of this result to the Burnside problem for semigroups.
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1972508
zbMATH Keywords: Burnside problem for semigroups
zbMATH Keywords: commutative semirings
zbMATH Keywords: finite chain property
zbMATH Keywords: finitely generated semigroups
zbMATH Keywords: growth functions
zbMATH Keywords: idempotent semirings
zbMATH Keywords: semigroups of matrices
zbMATH Keywords: tropical semirings
zbMATH Keywords: weak permutation property
MaRDI profile type: Publication
full work available at URL: s00233-001-0002-0
OpenAlex ID: W2074464903
DOI: 10.1007/S00233-001-0002-0
description: scientific article; zbMATH DE number 1972508