Identifying Orbit Lengths for Promotion

2025/06/27 by Catania, Elise, Kendrick, Jack, Russell, Heather M. +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.22306

Abstract

In this work we study Schützenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as m-diagrams. In particular, we prove that certain internal structures of SYT are preserved under promotion and correspond to distinct components of m-diagrams. By treating these structures as atomic parts of the m-diagram, we provide a simple algorithm for computing the promotion orbit length of rectangular SYT. We conclude the paper by applying our results to (column) semi-standard Young tableaux and prove a formula for the promotion orbit lengths of rectangular (column) SSYT.

Citations

• Rotation-invariant web bases from hourglass plabic graphs
• Promotion on oscillating and alternating tableaux and rotation of\n matchings and permutations
• Minimal orbits of promotion
• Cyclic sieving, rotation, and geometric representation theory
• A uniform bijection between nonnesting and noncrossing partitions
• A simple bijection between standard (n,n,n) tableaux and irreducible\n webs for sl₃
• Promotion and cyclic sieving via webs

Cited by

• Orbit lengths for promotion on 2-row and near-hook tableaux

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• Orbit lengths for promotion on 2-row and near-hook tableaux
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• Tableau Stabilization and Rectangular Tableaux Fixed by Promotion Powers