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Equivalence Relations Defined by Numbers of Occurrences of Factors

Saarela A.

Fundamenta Informaticae

2016

Vol. 145, nr 3

385--397

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.