Fixed points of endomorphisms over special confluent rewriting systems.
type: Item
instance of: scholarly article
title: Fixed points of endomorphisms over special confluent rewriting systems.
zbMATH Open document ID: 1236.20063
author: Pedro V. Silva
published in: Monatshefte für Mathematik
publication date: 2010-11-12T00:00:00Z
review text: Monoids defined by special confluent rewriting systems have been studied through an approach that preserves some of the properties of the case of free groups and contains the particular case of free products of cyclic groups. Cayley graphs of these monoids are known to be hyperbolic and to have a compact completion for the prefix metric. In this very interesting and well written paper, the author pursues this approach to investigate the dynamics of finite and infinite fixed point submonoids for two important classes of monoid endomorphisms: boundary-injective endomorphisms and bounded length decrease endomorphisms. He does this by using automata-theoretic, combinatorial, and topological techniques. In particular, he introduces and explores the automata-theoretic, not known to be decidable, property of finite-splitting for endomorphisms.
reviewed by: F. Blanchet-Sadri
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 20F67
Mathematics Subject Classification ID: 68Q42
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 68Q70
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 5815567
zbMATH Keywords: monoid endomorphisms
zbMATH Keywords: fixed points
zbMATH Keywords: special confluent rewriting systems
zbMATH Keywords: free products of cyclic groups
zbMATH Keywords: Cayley graphs
MaRDI profile type: Publication
full work available at URL: s00605-009-0124-0
OpenAlex ID: W2145237320
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DOI: 10.1007/S00605-009-0124-0
description: scientific article; zbMATH DE number 5815567