Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages

摘要

In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u ∈ ∑~+, 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 p~m q~n 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.