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In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are 'rich' in palindromes in the utmost sense. A characteristic property of so-called rich words is that all complete returns to any palindromic factor are themselves palindromes. These words encompass the well-known episturmian words, originally… (More)

Considering each occurence of a word w in a reccurent innnite word, we deene the set of return words of w to be the set of all distinct words beginning with an occurence of w and ending exactly just before the next occurence of w in the innnite word. We give a simpler proof of the recent result (of the second author) that for each factor w of a Sturmian… (More)

In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are… (More)

In this paper, we characterize by lexicographic order all finite Sturmian and epistur-mian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a wide sense (episturmian and episkew infinite words). That is, we characterize the set of all infinite words whose factors are… (More)