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- W3039087745 abstract "Two finite words are k-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most k with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The k-binomial complexity of an infinite word $$mathbf {x}$$ maps the integer n to the number of classes in the quotient, by this k-binomial equivalence relation, of the set of factors of length n occurring in $$mathbf {x}$$ . This complexity measure has not been investigated very much. In this paper, we characterize the k-binomial complexity of the Thue–Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue–Morse word is aperiodic, its k-binomial complexity eventually takes only two values. In this paper, we first express the number of occurrences of subwords appearing in iterates of the form $$varPsi ^ell (w)$$ for an arbitrary morphism $$varPsi $$ . We also thoroughly describe the factors of the Thue–Morse word by introducing a relevant new equivalence relation." @default.
- W3039087745 created "2020-07-10" @default.
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- W3039087745 date "2019-01-01" @default.
- W3039087745 modified "2023-09-26" @default.
- W3039087745 title "Computing the k-binomial Complexity of the Thue–Morse Word" @default.
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- W3039087745 doi "https://doi.org/10.1007/978-3-030-24886-4_21" @default.
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