A1 Refereed original research article in a scientific journal
Equivalence Relations Defined by Numbers of Occurrences of Factors
Authors: Saarela Aleksi
Publisher: IOS PRESS
Publication year: 2016
Journal: Fundamenta Informaticae
Journal name in source: FUNDAMENTA INFORMATICAE
Journal acronym: FUND INFORM
Volume: 145
Issue: 3
First page : 385
Last page: 397
Number of pages: 13
ISSN: 0169-2968
DOI: https://doi.org/10.3233/FI-2016-1367
Abstract
We study the question of what can be said about a word based on the numbers of occurrences of certain factors in it. We do this by defining a family of equivalence relations that generalize the so called k-abelian equivalence. The characterizations and answers we obtain are linear algebraic. We also use these equivalence relations to help us in solving some problems related to repetitions and palindromes, and to point out that some previous results about Sturmian words and k-abelian equivalence hold in a more general form.
We study the question of what can be said about a word based on the numbers of occurrences of certain factors in it. We do this by defining a family of equivalence relations that generalize the so called k-abelian equivalence. The characterizations and answers we obtain are linear algebraic. We also use these equivalence relations to help us in solving some problems related to repetitions and palindromes, and to point out that some previous results about Sturmian words and k-abelian equivalence hold in a more general form.
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