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Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2008/10/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Automata and Formal Language Theory
primitive word, square-free word, principal congruence, disjunctive language,
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In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u ∈Σ+, every element of λ(cp(u)) is d-primitive iff it is square-free, where cp(u) is the set of all cyclic-permutations of u, and λ(cp(u)) is the set of all primitive roots of it. Next we show that pmqn is a primitive word for every n, m ≥1 and primitive words p, q, under the condition that |p| = |q| and (m, n) ≠ (1, 1). We also give a condition of disjunctiveness for a language.