Geodesic
Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions
Pavel Galashin1 ; Darij Grinberg1 ; Gaku Liu1
1Massachusetts Institute of Technology
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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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 $2$.
DOI : 10.37236/5737
Classification : 05E05, 05E10, 14M15
Mots-clés : dual stable Grothendieck polynomials, symmetric functions, Schur functions, plane partitions, Young tableaux

Pavel Galashin  1   ; Darij Grinberg  1   ; Gaku Liu  1

1 Massachusetts Institute of Technology 
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     author = {Pavel Galashin and Darij Grinberg and Gaku Liu},
     title = {Refined dual stable {Grothendieck} polynomials and generalized {Bender-Knuth} involutions},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/5737},
     zbl = {1344.05148},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5737/}
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Pavel Galashin; Darij Grinberg; Gaku Liu. Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5737

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