An iterative formula for the Kostka-Foulkes polynomials

Abstract

An iterative formula for the Kostka-Foulkes polynomials is given using the vertex operator realization of the Hall-Littlewood polynomials. The operational formula can handle large Kostka-Foulkes polynomials, and a stability property for the Kostka-Foulkes polynomials is shown. We also use our algorithm to give a formula of $K_{\lambda \mu }(t)$ for $\mu$ being hook-shaped.

10 pages; final version (revised version with new title. New hook-shaped formula and stability property are added)

References in corpus (1)

• A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows

Cited by in corpus (1)

• The Green polynomials via vertex operators