Some non finitely generated monoids of repetition-free endomorphisms.
type: Item
instance of: scholarly article
title: Some non finitely generated monoids of repetition-free endomorphisms.
zbMATH Open document ID: 1042.68070
DOI: 10.1016/S0020-0190(02)00354-X
author: Yanyan Li
published in: Information Processing Letters
publication date: 2003-01-21T00:00:00Z
review text: We answer a question raised by Mitrana in Information Processing Letters 64 about primitive morphisms, that is, morphisms that preserve primitiveness of words. Given an alphabet \(A\) with \(\text{Card} (A)\geqslant2\), the monoid of primitive endomorphisms on \(A\) and the monoid of primitive uniform endomorphisms on \(A\) are not finitely generated. Moreover we show that it is also the case for the following monoids: the monoid of overlap-free (uniform) endomorphisms on \(A\) (when \(\text{Card} (A)\geqslant3)\), the monoid of \(k\)-power-free (uniform) endomorphisms on \(A\) (when \(\text{Card} (A)\geqslant2\) and \(k\geqslant3)\).
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 1856509
zbMATH Keywords: Formal languages
zbMATH Keywords: Combinatorics on words
zbMATH Keywords: Primitive words
zbMATH Keywords: Morphisms
MaRDI profile type: Publication
cites work: Q4941509
cites work: Avoidable patterns in strings of symbols
cites work: Uniformly growing k-th power-free homomorphisms
cites work: Sharp characterizations of squarefree morphisms
cites work: Q3912049
cites work: Q4723969
cites work: Primitive morphisms
cites work: Characterization of test-sets for overlap-free morphisms
cites work: Overlap-free morphisms and finite test-sets
cites work: Some results on \(k\)-power-free morphisms
cites work: A test-set fork-power-free binary morphisms
full work available at URL: s0020-0190(02)00354-x
OpenAlex ID: W1965932039
description: scientific article; zbMATH DE number 1856509