Identifying Orbit Lengths for Promotion
arXiv:2506.22306
Abstract
In this work we study Schützenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as diagrams. In particular, we prove that certain internal structures of SYT are preserved under promotion and correspond to distinct components of diagrams. By treating these structures as atomic parts of the 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.