Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$

18 Oct 2019 Qiu Dun Remmel Jeffrey

Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of 132-avoiding permutations and the set of 123-avoiding permutations...

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