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We study the descent distribution over the set of centrosymmetricpermutations that avoid the pattern of length 3. Our main tool in the mostpuzzling case, namely, $\tau=123$ and $n$ even, is a bijection that associatesa Dyck prefix of length $2n$ to every centrosymmetric permutation in $S_{2n}$that avoids 123.

The Eulerian numbers on restricted centrosymmetric permutations