Pavel Galashin ; Darij Grinberg ; Gaku Liu
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Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions
dmtcs:6374 -
Discrete Mathematics & Theoretical Computer Science,
April 22, 2020,
DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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https://doi.org/10.46298/dmtcs.6374
Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutionsArticle
Authors: Pavel Galashin 1; Darij Grinberg 1; Gaku Liu 1
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Pavel Galashin;Darij Grinberg;Gaku Liu
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.