Polynomial Expressions for Symmetric Group Characters on Cycles

Abstract

In \cite{[CZ]}, Cohen and Zemel showed that for a partition $\hat{I}»⊢k$, the dimension of the irreducible representation of $S_n$ corresponding to the partition $(n-k,\hat{I}»)⊢n$ is a polynomial of degree $k$ in $n$, whose coefficients in the binomial basis count standard Young tableaux of shape $\hat{I}»$ with special restrictions. In this paper, we generalize their results on the representation's dimension to character values on arbitrary cycles.

18 pages