Séminaire Lotharingien de Combinatoire, 84B.15 (2020), 12 pp.
Valentin Buciumas, Travis Scrimshaw and Katherine Weber
Colored Five-Vertex Models and Lascoux Polynomials and Atoms
Abstract.
We construct an integrable colored five-vertex model whose partition function is a Lascoux atom based on the five-vertex model of Motegi and Sakai and the colored five-vertex model of Brubaker, the first author, Bump, and Gustafsson.
We then modify this model in two different ways to construct a Lascoux polynomial, yielding the first known proven combinatorial interpretation of a Lascoux polynomial and atom.
Using this, we prove a conjectured combinatorial interpretation in terms of set-valued tableaux of a Lascoux polynomial and atom due to Pechenik and the second author.
We also prove the combinatorial interpretation of the Lascoux atom using set-valued skyline tableaux of Monical.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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