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Séminaire Lotharingien de Combinatoire, 84B.19 (2020), 12 pp.

# Oliver Pechenik and Travis Scrimshaw

# K-theoretic Crystals for Set-Valued Tableaux of Rectangular Shapes

**Abstract.**
With C. Monical (2018), we introduced a notion of K-crystals and conjectured they exist for all rectangular shapes λ.
Here, we establish this conjecture, yielding the first combinatorial formula (as the sum over flagged set-valued tableaux) for the Lascoux polynomials
*L*_{wλ}. We then prove corresponding cases of conjectures of Ross-Yong (2015) and Monical (2016).

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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