A1 Refereed original research article in a scientific journal
A characterization of free pairs of upper triangular free monoid morphisms
Authors: Juha Honkala
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2019
Journal:Information and Computation
Journal acronym: INFORM COMPUT
Volume: 267
First page : 110
Last page: 115
Number of pages: 6
ISSN: 0890-5401
eISSN: 1090-2651
DOI: https://doi.org/10.1016/j.ic.2019.03.007
Abstract
We study combinatorics on morphisms. More precisely, we study free monoid morphisms and their freeness properties. By definition, a set F of endomorphisms of a free monoid is free, if every product formed of morphims from F can be uniquely factorized. We show that if f and g are endomorphisms of the free monoid A* having upper triangular incidence matrices with diagonal entries at least two, then the pair {f, g} is free if and only if f and g do not commute. This result implies that for such pairs freeness is very easy to decide. (C) 2019 Elsevier Inc. All rights reserved.
We study combinatorics on morphisms. More precisely, we study free monoid morphisms and their freeness properties. By definition, a set F of endomorphisms of a free monoid is free, if every product formed of morphims from F can be uniquely factorized. We show that if f and g are endomorphisms of the free monoid A* having upper triangular incidence matrices with diagonal entries at least two, then the pair {f, g} is free if and only if f and g do not commute. This result implies that for such pairs freeness is very easy to decide. (C) 2019 Elsevier Inc. All rights reserved.
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