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arXiv · 1909.12833

Combinatorial relations on skew Schur and skew stable Grothendieck polynomials

Melody Chan·Nathan Pflueger
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Abstract

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 L\'opez Mart\'in 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.

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Melody Chan, Nathan Pflueger. 2019-09-26. Combinatorial relations on skew Schur and skew stable Grothendieck polynomials. https://arxiv.org/abs/1909.12833

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