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A monoid of Kostka–Foulkes polynomials

  • Pasquale Petrullo
  • Domenico SenatoEmail author
Article
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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.

Keywords

Kostka–Foulkes polynomials Kostant partition function Raising operators Triangular matrices 

Mathematics Subject Classification

05E05 05E10 06A11 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Informatica e EconomiaUniversità degli Studi della BasilicataPotenzaItaly

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