A monoid of Kostka–Foulkes polynomials

Abstract

We introduce the monoid of the admissible KF polynomials. These polynomials are invariant under uniform translation of partitions. Moreover, each Kostka–Foulkes polynomial turns out to be a linear combination of admissible KF polynomials with coefficients $$-1$$ or 1. Elementary manipulations of triangular matrices provide identities on Kostka–Foulkes polynomials which are not obvious a priori.