Refined Dual Stable Grothendieck Polynomials and Generalized Bender-Knuth Involutions

  • Pavel Galashin
  • Darij Grinberg
  • Gaku Liu
Keywords: Dual stable Grothendieck polynomials, Symmetric functions, Schur functions, Plane partitions, Young tableaux


The dual stable Grothendieck polynomials are a deformation of the Schur functions, 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 $2$.
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