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Set-Valued Skyline Fillings

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arxiv 1611.08777 v1 pith:GDGSOTGM submitted 2016-11-27 math.CO

Cara Monical This is my paper · ORCID
classification math.CO
keywords set-valuedfillingssemistandardskylinecombinatorialgivetableauxadditionally
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Square root crystals and the square root of $B(\infty)$

    math.RT 2026-08 conditional novelty 8.0 of 10

    A square root analog of B(∞) is constructed from set-valued tableaux, with Lusztig-type, polyhedral, and string descriptions, and a product character formula.

  2. Grothendieck positivity for normal square root crystals

    math.CO 2025-01 conditional novelty 8.0 of 10

    Every finite normal square root crystal has a character equal to a nonnegative integer combination of symmetric Grothendieck polynomials, indexed by its highest weight elements.

  3. Colored five-vertex models and Lascoux polynomials and atoms

    math.CO 2019-08 accept novelty 8.0 of 10

    A colored five-vertex model has Lascoux atom and polynomial partition functions, proving the Pechenik-Scrimshaw and Monical set-valued tableau conjectures.

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