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. 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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Markov Chains and Monte Carlo Methods
Algebraic structures and combinatorial models
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 3
- Publication date
- 28 August 2026
- Language
- EN