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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