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

Abstract

In this note, we provide a short proof of Theorem 3.3 in the paper titled 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 give a short proof of their result which extends to skew shapes.

Skew Schur Polynomials and Cyclic Sieving Phenomenon

“…. , q k−1 ) is a CSP polynomial modulo m. It was shown in [1] that this is true in case where (k, m(|λ| − |µ|)) = 1. However, one can find a counterexample in case where k is not divisible by m and (k, m(|λ| − |µ|)) = 1.…”