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We prove some new combinatorial properties of the set PER of all words w having two periods p and q which are coprimes and such that w = p + q-2 [4,3]. We show that aPERb U {a, b} = St n Lynd, where St is the set of the finite factors of all infinite Sturmian words and Lynd is the set of the Lyndon words on the alphabet {a, b}. It is also shown that aPERb U… (More)

We consider involutory antimorphisms ϑ of a free monoid A * and their fixed points, called ϑ-palindromes or pseudopalindromes. A ϑ-palindrome reduces to a usual palindrome when ϑ is the reversal operator. For any word w ∈ A * the right (resp. left) ϑ-palindrome closure of w is the shortest ϑ-palindrome having w as a prefix (resp. suffix). We prove some… (More)

In this paper we consider the following question in the spirit of Ramsey theory: Given x ∈ A ω , where A is a finite non-empty set, does there exist a finite coloring of the non-empty factors of x with the property that no factorization of x is monochromatic? We prove that this question has a positive answer using two colors for almost all words relative to… (More)