Séminaire Lotharingien de Combinatoire, 89B.16 (2023), 12 pp.
Ben Adenbaum and Sergi Elizalde
Rowmotion on 321-Avoiding Permutations
Abstract.
We give a natural definition of rowmotion for 321-avoiding permutations, by translating, through bijections involving Dyck paths and the Lalanne-Kreweras involution, the analogous notion for antichains of the positive root poset of type A. We prove that some permutation statistics, such as the number of fixed points, are homomesic under rowmotion, meaning that they have a constant average over its orbits.
Finally, we show that the Armstrong--Stump--Thomas equivariant bijection between antichains in types A and B and non-crossing matchings can be described more naturally in terms of the Robinson-Schensted-Knuth correspondence on permutations.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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