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A centrosymmetric permutation is one which is invariant under thereverse-complement operation, or equivalently one whose associated standardYoung tableaux under the Robinson-Schensted algorithm are both invariant underthe Schutzenberger involution. In this paper, we characterize the set ofpermutations avoiding 1243 and 2143 whose images under the reverse-complementmapping also avoid these patterns. We also characterize in a simple manner thecorresponding Schroder paths under a bijection of Egge and Mansour. We then usethese results to enumerate centrosymmetric permutations avoiding the patterns1243 and 2143. In a similar manner, centrosymmetric involutions avoiding thesesame patterns are shown to be enumerated by the Pell numbers.

Centrosymmetric Permutations and Involutions Avoiding 1243 and 2143