Permutations avoiding a pattern from $S_k$ and at least two patterns from $S_3$

Abstract

In this paper, we find explicit formulas or generating functions for the cardinalities of the sets $S_n(T,\tau )$ of all permutations in $S_n$ that avoid a pattern $\tau \in S_k$ and a set $T$, $|T|\ge 2$, of patterns from $S_3$. The main body of the paper is divided into three sections corresponding to the cases $|T|=2,3$ and $|T|\ge 4$. As an example, in the fifth section, we obtain the complete classification of all cardinalities of the sets $S_n(T,\tau )$ for $k=4$.

13 pages, 1 table