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arXiv · 1002.1229

Centrosymmetric Permutations and Involutions Avoiding 1243 and 2143

Mark F. Flanagan·Matteo Silimbani
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Abstract

A centrosymmetric permutation is one which is invariant under the reverse-complement operation, or equivalently one whose associated standard Young tableaux under the Robinson-Schensted algorithm are both invariant under the Schutzenberger involution. In this paper, we characterize the set of permutations avoiding 1243 and 2143 whose images under the reverse-complement mapping also avoid these patterns. We also characterize in a simple manner the corresponding Schroder paths under a bijection of Egge and Mansour. We then use these results to enumerate centrosymmetric permutations avoiding the patterns 1243 and 2143. In a similar manner, centrosymmetric involutions avoiding these same patterns are shown to be enumerated by the Pell numbers.

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Mark F. Flanagan, Matteo Silimbani. 2011-02-03. Centrosymmetric Permutations and Involutions Avoiding 1243 and 2143. https://arxiv.org/abs/1002.1229

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