# ALGEBRAIC COMBINATORICS

Combinatorial relations on skew Schur and skew stable Grothendieck polynomials
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.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.144
Classification: 05E05,  05E14
Keywords: Schur functions, Grothendieck polynomials, insertion algorithms, set-valued tableaux, Brill–Noether theory.
@article{ALCO_2021__4_1_175_0,
author = {Chan, Melody and Pflueger, Nathan},
title = {Combinatorial relations on skew Schur and skew stable Grothendieck polynomials},
journal = {Algebraic Combinatorics},
pages = {175--188},
publisher = {MathOA foundation},
volume = {4},
number = {1},
year = {2021},
doi = {10.5802/alco.144},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.144/}
}
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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