On complementary triples of Sturmian bisequences. (English) Zbl 0862.68085

Summary: A Sturmian bisequence \(S\) is a subset of \(\mathbb{Z}\) such that the numbers of elements of \(S\) in any two intervals of equal lengths differ by at most 1. A complementary triple of bisequences is a set of three bisequences such that every integer belongs to exactly one bisequence. In the paper a question of Loeve is answered by giving a characterization of all complementary triples of Sturmian bisequences.


68R15 Combinatorics on words
20M05 Free semigroups, generators and relations, word problems
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