Permutations Restricted by Two Distinct Patterns of Length Three

Abstract

Define $S_n(R;T)$ to be the number of permutations on $n$ letters which avoid all patterns in the set $R$ and contain each pattern in the multiset $T$ exactly once. In this paper we enumerate $S_n(\{\alpha \};\{\beta \})$ and $S_n(\varnothing ;\{\alpha ,\beta \})$ for all $\alpha \ne \beta \in S_3$. The results for $S_n(\{\alpha \};\{\beta \})$ follow from two papers by Mansour and Vainshtein.

15 pages, some relevant reference brought to my attention (see section 4)