Abstract
The binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. Based on this classical notion, we introduce the m-binomial equivalence of two words refining the abelian equivalence. The m-binomial complexity of an infinite word x maps an integer n to the number of m-binomial equivalence classes of factors of length n occurring in x. We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue–Morse word. We also mention the possible avoidance of 2-binomial squares.
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Rigo, M., Salimov, P.: Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words (long version) (preprint, 2013), http://hdl.handle.net/2268/149313
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Rigo, M., Salimov, P. (2013). Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds) Combinatorics on Words. Lecture Notes in Computer Science, vol 8079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40579-2_23
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DOI: https://doi.org/10.1007/978-3-642-40579-2_23
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