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The expected shape of random doubly alternating Baxter permutations

Theodore Dokos1, Igor Pak1
1DEPARTMENT OF MATHEMATICS, UCLA, LOS ANGELES, CALIFORNIA, USA

Abstract

Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e., Baxter permutations σSn, such that σ and σ1 are alternating. They proved that the number of such permutations in S2n and S2n+1 is the Catalan number Cn. In this paper, we compute the expected limit shape of such permutations, following the approach by Miner and Pak.

Keywords: Baxter permutations, Catalan numbers