Refined dual stable grothendieck polynomials and generalized bender-knuth involutions

Pavel Galashin, Gaku Liu, Darij Grinberg

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The dual stable Grothendieck polynomials are a deformation of the Schur func- tions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and we prove that this generalization still defines symmetric functions. For this fact, we give two self-contained proofs, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume23
Issue number3
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016, Australian National University. All rights reserved.

Keywords

  • Bender-knuth involutions
  • Dual stable grothendieck polynomials
  • Reverse plane partitions
  • Symmetric functions

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