Free action and cyclic sieving on skew semi-standard Young tableaux

TL;DR

This paper offers a concise proof of a cyclic sieving phenomenon related to semi-standard Young tableaux and extends the result to skew shapes, enhancing understanding of symmetry in combinatorial objects.

Contribution

Provides a simplified proof of an existing theorem and generalizes the cyclic sieving phenomenon to skew semi-standard Young tableaux.

Findings

Short proof of Theorem 3.3 from prior work

Extension of cyclic sieving to skew shapes

Enhanced understanding of symmetry in tableaux

Abstract

In this note, we provide a short proof of Theorem 3.3 in the paper titled \emph{Crystals, semistandard tableaux and cyclic sieving phenomenon}, by Y.-T.~Oh and E.~Park, which concerns a cyclic sieving phenomenon on semi-standard Young tableaux. We also extend the result to skew shapes.