Fixed points of endomorphisms of trace monoids.
Given an alphabet \(A\) and a symmetric anti-reflexive relation \(I\) on \(A\), the corresponding \textit{trace monoid} is given by presentation \(\langle A:ab=ba,\;(a,b)\in I\rangle\). In the paper under review it is shown that the fixed point submonoid and the periodic point submonoid associated to an endomorphism of a trace monoid over a finite alphabet are always finitely generated. The second main result of the paper addresses the question of rationality for fixed point monoids. It is shown that rationality for all endomorphisms is equivalent to the requirement for the original trace monoid to be a free product of free commutative monoids.
scientific article; zbMATH DE number 6363670
scientific article