Séminaire Lotharingien de Combinatoire, 78B.35 (2017), 12 pp.

Cara Monical

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 we then give analogues of results of J. Haglund, K. Luoto, S. Mason, and S. van Willigenburg. Additionally, we give a bijection between set-valued semistandard Young tableaux and C. Lenart's Schur expansion of the Grothendieck polynomial Gλ, using the uncrowding operator of V. Reiner, B. Tenner, and A. Yong.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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