Combinatorial relations on skew Schur and skew stable Grothendieck polynomials
Combinatorics
2020-09-15 v2
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.
Keywords
Cite
@article{arxiv.1909.12833,
title = {Combinatorial relations on skew Schur and skew stable Grothendieck polynomials},
author = {Melody Chan and Nathan Pflueger},
journal= {arXiv preprint arXiv:1909.12833},
year = {2020}
}
Comments
13 pages, to appear in Algebraic Combinatorics. arXiv admin note: substantial text overlap with arXiv:1708.09378