Séminaire Lotharingien de Combinatoire, 93B.83 (2025), 12 pp.
Elise Catania, Jack Kendrick, Heather M Russell and Julianna S Tymoczko
Identifying Orbit Lengths for Promotion
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.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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