Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions

Pavel Galashin (1) , Darij Grinberg (1) , Gaku Liu (1)

1 Department of Mathematics [MIT]

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 such that the generalization still defines symmetric functions. We outline two self-contained proofs of this fact, 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.

Domaines: Combinatoire [math.CO]

Pavel Galashin, Darij Grinberg, Gaku Liu. Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6374⟩. ⟨hal-02168300⟩