Set-Valued Skyline Fillings

Abstract

Set-valued tableaux play an important role in combinatorial $K$-theory. Separately, semistandard skyline fillings are a combinatorial model for Demazure atoms and key polynomials. We unify these two concepts by defining a set-valued extension of semistandard skyline fillings and then give analogues of results of J. Haglund, K. Luoto, S. Mason, and S. van Willigenberg. Additionally, we give a bijection between set-valued semistandard Young tableaux and C. Lenart's Schur expansion of the Grothendieck polynomial $G_{\lambda }$, using the uncrowding operator of V. Reiner, B. Tenner, and A. Yong.

17 pages

References in corpus (1)

• A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm

Cited by in corpus (1)

• Newton polytopes and symmetric Grothendieck polynomials