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Combinatorial relations on skew Schur and skew stable Grothendieck polynomials
Chan, Melody1; Pflueger, Nathan2
1 Brown University Department of Mathematics Box 1917 Providence RI 02912, USA
2 Amherst College Department of Mathematics and Statistics Amherst MA 01002, USA
Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 175-188.

We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies some previous results: it generalizes a combinatorial formula obtained in earlier joint work with López Martín and Teixidor i Bigas concerning Brill–Noether curves, and it generalizes a 2000 formula of Lenart and a recent result of Reiner–Tenner–Yong to skew shapes. We also give an expansion in the other direction: expressing skew Schur functions in terms of skew Grothendieck polynomials.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.144
Classification: 05E05, 05E14
Keywords: Schur functions, Grothendieck polynomials, insertion algorithms, set-valued tableaux, Brill–Noether theory.

Chan, Melody 1; Pflueger, Nathan 2

1 Brown University Department of Mathematics Box 1917 Providence RI 02912, USA
2 Amherst College Department of Mathematics and Statistics Amherst MA 01002, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chan, Melody; Pflueger, Nathan. Combinatorial relations on skew Schur and skew stable Grothendieck polynomials. Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 175-188. doi : 10.5802/alco.144. https://alco.centre-mersenne.org/articles/10.5802/alco.144/

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