## Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions.(English)Zbl 1344.05148

Summary: 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.

### MSC:

 05E05 Symmetric functions and generalizations 05E10 Combinatorial aspects of representation theory 14M15 Grassmannians, Schubert varieties, flag manifolds
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### References:

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