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Puzzles in
$K$-homology of Grassmannians
Pavlo Pylyavskyy and Jed Yang |
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Vol. 303 (2019), No. 2, 703–727
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Abstract |
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Knutson, Tao, and Woodward (2004) formulated a Littlewood–Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil (2006) and Wheeler and Zinn-Justin (2017) have found additional triangular puzzle pieces that allow one to express structure constants for -theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlewood–Richardson rule for -homology of Grassmannians. We also explore the corresponding eight versions of -theoretic Littlewood–Richardson tableaux. |
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Keywords
puzzles, hexagon, tiling, K-theory, Grassmannian,
Littlewood–Richardson coefficient
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Mathematical Subject Classification 2010
Primary: 05E15
Secondary: 14M15, 52C20
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Milestones
Received: 3 April 2018
Revised: 3 March 2019
Accepted: 1 May 2019
Published: 4 January 2020
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Authors |
| Pavlo Pylyavskyy | |
| Department of Mathematics University of Minnesota Minneapolis United States |
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| Jed Yang | |
| Department of Mathematics and
Computer Science Bethel University St Paul, MN United States |
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