Séminaire Lotharingien de Combinatoire, 85B.4 (2021), 12 pp.

Connor Ahlbach, Jacob David, Suho Oh and Christopher Wu

Tableau Stabilization and Lattice Paths

Abstract. If one attaches shifted copies of a skew tableau to the right of itself and rectifies, at a certain point the copies no longer experience vertical slides, a phenomenon called tableau stabilization. While tableau stabilization was originally developed to construct the sufficiently large rectangular tableaux fixed by given powers of promotion, the purpose of this extended abstract is to improve the original bound on tableau stabilization to the number of rows of the skew tableau. In order to prove this bound, we encode increasing subsequences as lattice paths and show that various operations on these lattice paths weakly increase the maximum combined length of the increasing subsequences.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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