Set-valued skyline fillings. (English. French summary) Zbl 1384.05160
Summary: 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 et al. [J. Comb. Theory, Ser. A 118, No. 2, 463–490 (2011; Zbl 1229.05270)]. 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 [“Poset edge densities, nearly reduced words, and barely set-valued tableaux”, Preprint, arXiv:1603.09589].
MSC:
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
Citations:
Zbl 1229.05270References:
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