Lyndon traces and shuffle algebras
type: Item
instance of: scholarly article
title: Lyndon traces and shuffle algebras
zbMATH Open document ID: 0818.20072
DOI: 10.1016/0022-4049(94)90118-X
author: Yuji Kobayashi
author: Masashi Katsura
published in: Journal of Pure and Applied Algebra
publication date: 1994-09-22T00:00:00Z
review text: Let \(A\) be an alphabet and let \(\vartheta\) be a symmetric subset of \(A\times A\). The partially commutative or trace monoid \(M(A, \vartheta)\) is then the monoid presented by \(\langle A\); \(ab= ba\), \((a,b)\in \vartheta\rangle\). The partially commutative algebra is the algebra, denoted \(K\langle A, \vartheta\rangle\), of formal linear combinations of traces of \(M(A, \vartheta)\). This paper is organized around the notion of Lyndon trace, introduced by Duchamp and Krob, which is a partially commutative generalization of the classical notion of Lyndon word. The authors give first several characterization results of Lyndon traces. They apply then their results in order to prove that the algebra \(K\langle A,\vartheta \rangle\), equipped with the partially commutative shuffle product, is a free commutative algebra freely generated by a family naturally associated with Lyndon traces. The paper ends with an enumeration of Lyndon traces, a result already obtained by Duchamp and Krob.
reviewed by: Daniel Krob
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 68Q70
zbMATH DE Number: 643792
zbMATH Keywords: trace monoids
zbMATH Keywords: partially commutative algebras
zbMATH Keywords: Lyndon words
zbMATH Keywords: Lyndon traces
zbMATH Keywords: partially commutative shuffle products
zbMATH Keywords: free commutative algebras
MaRDI profile type: Publication
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full work available at URL: 0022-4049(94)90118-x
OpenAlex ID: W2062005678
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description: scientific article; zbMATH DE number 643792