Maximal pattern complexity of words over l letters

Authors:
Teturo Kamae;Rao Hui
Affiliations:
Department of Mathematics, Osaka City University, Japan;Department of Mathematics, Tsinghua University, Beijing, PR China
Venue:
European Journal of Combinatorics
Year:
2006

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Abstract

The maximal pattern complexity function p*α (k) of an infinite word α = α0α1α2... over l letters, is introduced and studied by [3, 4].In the present paper we introduce two new techniques, the ascending chain of alphabets and the singular decomposition, to study the maximal pattern complexity. It is shown that if p*α(k) lk holds for some k ≥ 1, then α is periodic by projection. Accordingly we define a pattern Sturmian word over l letters to be a word which is not periodic by projection and has maximal pattern complexity function p*α(k) = lk. Two classes of pattern Sturmian words are given. This generalizes the definition and results of [3] where l = 2.