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.
Pattern avoiding and q-decreasing binary words / Barcucci, Elena; Bernini, Antonio; Bilotta, Stefano; Pinzani, Renzo. - In: RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS. - ISSN 0988-3754. - ELETTRONICO. - 59:(2025), pp. 13.0-13.0. [10.1051/ita/2025013]
Pattern avoiding and q-decreasing binary words
Barcucci, ElenaMembro del Collaboration Group
;Bernini, AntonioMembro del Collaboration Group
;Bilotta, Stefano
Membro del Collaboration Group
;Pinzani, RenzoMembro del Collaboration Group
2025
Abstract
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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