English

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