Order and quasiperiodicity in episturmian words
نویسنده
چکیده
In this paper, we build upon previous work concerning inequalities characterizing Sturmian and episturmian words – see [19, 29, 30, 14, 16]. First let us recall from [29] the following notion relating to lexicographic order. Let A be a totally ordered finite alphabet consisting of at least two letters. To any infinite word x over A, we can associate two infinite words min(x) and max(x) such that any prefix of min(x) (resp. max(x)) is the lexicographically smallest (resp. greatest) amongst the factors of x of the same length. More precisely, if we denote by min(x|k) (resp. max(x|k)) the lexicographically smallest (resp. greatest) factor of x of length k for the given order, then min(x|k) and max(x|k) are clearly prefixes of the respective words min(x|k + 1) and max(x|k + 1). So we can define, by taking limits, the following two infinite words
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