Symmetries of the partial order of traces
type: Item
instance of: scholarly article
title: Symmetries of the partial order of traces
zbMATH Open document ID: 0954.06013
DOI: 10.1023/A:1006379732338
author: Dietrich Kuske
published in: Order
publication date: 2000-06-21T00:00:00Z
review text: Free partially commutative monoids, also called trace monoids, were introduced by \textit{P. Cartier} and \textit{D. Foata} [Problèmes combinatoires de commutation et réarrangements (Lect. Notes Math. 85) (Springer, Berlin) (1969; Zbl 0186.30101)]. There is a broad research on this topic in theoretical computer science. The main results of the author are the following. If \(G\) is a group, there exists a trace monoid whose partial order has the automorphism group isomorphic to \(G\). In the case of finitely generated trace monoids these groups are profinite and possess only finitely many finite simple decomposition factors. Also the partial order associated with the Rado graph as dependence alphabet does not give rise to a homogeneous domain, which answers an open question of \textit{P. Boldi}, \textit{F. Cardone} and \textit{N. Sabadini} [in: M. Droste et al. (eds.), Semantics of programming languages and model theory (Gordon and Breach Sci. Publ., Yverdon), Algebra Log. Appl. 5, 89-108 (1993; Zbl 0803.68035)].
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 1463097
zbMATH Keywords: free partially commutative monoids
zbMATH Keywords: trace monoids
zbMATH Keywords: partial order
zbMATH Keywords: automorphism group
zbMATH Keywords: Rado graph
MaRDI profile type: Publication
full work available at URL: a:1006379732338
OpenAlex ID: W104166885
description: scientific article; zbMATH DE number 1463097