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- W4288365712 abstract "In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of semistandard set-valued tableaux of any fixed rectangular shape. Here, we establish this conjecture by explicitly constructing the K-crystal operators. As a consequence, we establish the first combinatorial formula for Lascoux polynomials $L_{wlambda}$ when $lambda$ is a multiple of a fundamental weight as the sum over flagged set-valued tableaux. Using this result, we then prove corresponding cases of conjectures of Ross--Yong (2015) and Monical (2016) by constructing bijections with the respective combinatorial objects." @default.
- W4288365712 created "2022-07-29" @default.
- W4288365712 creator A5058699487 @default.
- W4288365712 creator A5087568902 @default.
- W4288365712 date "2019-04-21" @default.
- W4288365712 modified "2023-09-25" @default.
- W4288365712 title "K-theoretic crystals for set-valued tableaux of rectangular shapes" @default.
- W4288365712 doi "https://doi.org/10.48550/arxiv.1904.09674" @default.
- W4288365712 hasPublicationYear "2019" @default.
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