Puzzles in $K$-homology of Grassmannians

Abstract

Knutson, Tao, and Woodward formulated a Littlewood-Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil and Wheeler-Zinn-Justin have found additional triangular puzzle pieces that allow one to express structure constants for $K$-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlewood-Richardson rule for $K$-homology of Grassmannians. We also explore the corresponding eight versions of $K$-theoretic Littlewood-Richardson tableaux.

18 pages, 8 figures

References in corpus (1)

• Genomic Tableaux

Cited by in corpus (2)

• Crystal structures for symmetric Grothendieck polynomials
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