Permutations containing a pattern exactly once and avoiding at least two patterns of three letters

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63258In this paper, we find an explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets $S_n(T;τ)$ of all permutations in $S_n$ that contain $τ\in S_k$ exactly once and avoid a subset $T\subseteq S_3$, $|T|\geq2$. The main body of the paper is divided into three sections corresponding to the cases $|T|=2,3$ and $|T|\geq4$.8 pagesCombinatoricsPermutations containing a pattern exactly once and avoiding at least two patterns of three letterstext