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A Wilf equivalence related to two stack sortable permutations

David Callan
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Abstract

A permutation is so-called two stack sortable if it (i) avoids the (scattered) pattern 2-3-4-1, and (ii) contains a 3-2-4-1 pattern only as part of a 3-5-2-4-1 pattern. Here we show that the permutations on [n] satisfying condition (ii) alone are equinumerous with the permutations on [n] that avoid the mixed scattered/consecutive pattern 31-4-2. The proof uses a known bijection from 3-2-1-avoiding to 3-1-2-avoiding permutations.

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David Callan. 2005-10-11. A Wilf equivalence related to two stack sortable permutations. https://arxiv.org/abs/math/0510211

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