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Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin–Roichman type. In this work, we construct a new involution on plane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the(More)
A cyclic polytope of dimension d with n vertices is a convex polytope combinato-rially equivalent to the convex hull of n distinct points on a moment curve in R d. In this paper, we prove the cyclic sieving phenomenon, introduced by Reiner-Stanton-White, for faces of an even-dimensional cyclic polytope, under a group action that cyclically translates the(More)
In this paper we present two interesting properties of 321-avoiding Baxter permutations. The first one is a variant of refined major-balance identity for the 321-avoiding Baxter permutations, respecting the number of fixed points and descents. The second one is a bijection between the 321-avoiding Baxter permutations with the entry 1 preceding the entry 2(More)
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