Journal of Combinatorics
Volume 13 (2022)
Tableau stabilization and lattice paths
Pages: 105 – 134
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 paper 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.
cyclic sieving, promotion, jeu-de-taquin, rectificaton, tableaux, stabilization, permutation
2010 Mathematics Subject Classification
Primary 05E10. Secondary 05E18.
Received 5 November 2020
Accepted 19 January 2021
Published 31 January 2022