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• W1605366104 abstract "We derive explicit Pieri-type multiplication formulas in the Grothendieck ring of a flag variety. These expand the product of an arbitrary Schubert class and a special Schubert class in the basis of Schubert classes. These special Schubert classes are indexed by a cycle which has either the form $(k{-}p{+}1,k{-}p{+}2,ldots ,k{+}1)$ or the form $(k{+}p,k{+}p{-}1,ldots ,k)$, and are pulled back from a Grassmannian projection. Our formulas are in terms of certain labeled chains in the $k$-Bruhat order on the symmetric group and are combinatorial in that they involve no cancellations. We also show that the multiplicities in the Pieri formula are naturally certain binomial coefficients." @default.
• W1605366104 created "2016-06-24" @default.
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• W1605366104 date "2006-12-19" @default.
• W1605366104 modified "2023-09-30" @default.
• W1605366104 title "A Pieri-type formula for the ${K}$-theory of a flag manifold" @default.
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• W1605366104 doi "https://doi.org/10.1090/s0002-9947-06-04043-8" @default.
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