Pattern avoiding and q -decreasing binary words - Barcucci, Elena; Bernini, Antonio; Bilotta, Stefano; Pinzani, Renzo (RAIRO. Informatique théorique et applications, 2025)
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 .