Colored five‐vertex models and Lascoux polynomials and atoms
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SCOPUS
- Title
- Colored five‐vertex models and Lascoux polynomials and atoms
- Authors
- Buciumas, Valentin; Scrimshaw, Travis; Weber, Katherine
- Date Issued
- 2020-12
- Publisher
- Oxford University Press
- 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 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 Monical's conjectured combinatorial interpretation of the Lascoux atom using set-valued skyline tableaux.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/120857
- DOI
- 10.1112/jlms.12347
- ISSN
- 0024-6107
- Article Type
- Article
- Citation
- Journal of the London Mathematical Society, vol. 102, no. 3, page. 1047 - 1066, 2020-12
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