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This study reveals a bijection of q-decreasing binary words and pattern avoiding ones, suggesting new mathematical connections.
We provide a bijection between the set of the q-decreasing binary words (in the case where q is an irreducible positive rational number) and a set of binary words avoiding some patterns whose lengths depends on the number q . Moreover, for such a set we give the details of the construction, the generating function according to the length of its words, and the recurrence relation of the enumerating sequence, depending on q .
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Barcucci et al. (2025) studied this question.
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