Some Plethystic Identites and Kostka-Foulkes polynomials

TL;DR

This paper explores the connections between Kostka-Foulkes polynomials and symmetric functions related to the q,t-Catalan series, revealing new identities and relationships in algebraic combinatorics.

Contribution

It introduces new plethystic identities linking Kostka-Foulkes polynomials with symmetric functions from the q,t-Catalan framework.

Findings

Derived new plethystic identities involving Kostka-Foulkes polynomials

Established connections between symmetric functions and q,t-Catalan series

Enhanced understanding of algebraic structures in combinatorics

Abstract

We investigate the relationship between Kostka-Foulkes polynomials and certain symmetric functions that arise from Garsia and Haglund's study of the q,t-Catalan series.