Permutations Containing a Pattern Exactly Once and Avoiding At Least Two Patterns of Three Letters

Abstract

In this paper, we find explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets \(S_{n}(T; \tau)\) of all permutations in \(S_n\) that contain \(\tau \in S_k\) exactly once and avoid a subset \(T \subseteq S_3\) where \(|T| \geq 2\).