Permutations Restricted by Two Distinct Patterns of Length Three

Details Permutations Restricted by Two Distinct Patterns of Length Three Permutations Restricted by Two Distinct Patterns of Length Three

2000-12-05

arxiv.org/abs/math/0012029v2

Mathematics

Combinatorics

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

Scientific paper

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 $S_n(\emptyset;\{\alpha,\beta\})$ for all $\alpha \neq \beta \in S_3$. The results for $S_n(\{\alpha\};\{\beta\})$ follow from two papers by Mansour and Vainshtein.

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