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

摘要

In this paper, we find an explicit formulas, or recurrences, in terms ofgenerating functions for the cardinalities of the sets $S_n(T;\tau)$ of allpermutations in $S_n$ that contain $\tau\in S_k$ exactly once and avoid asubset $T\subseteq S_3$, $|T|\geq2$. The main body of the paper is divided intothree sections corresponding to the cases $|T|=2,3$ and $|T|\geq4$.