Séminaire Lotharingien de Combinatoire, 93B.107 (2025), 12 pp.
Ilani Axelrod-Freed, Jiyang Gao and Sylvester W. Zhang
Rhombic Tableaux for Partial Flag Varieties
Abstract.
We introduce semi-standard rhombic tableaux as a new combinatorial model for Schubert polynomials corresponding to cohomology classes of a partial flag variety. Based on Elnitsky's rhombic tilings, our model generalizes semi-standard Young tableaux in the case of Grassmannian. Our construction naturally extends to infinite flag varieties (Stanley symmetric functions) and to K-theory using set-valued tableaux. We also discuss a generalization of Bender-Knuth involution.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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