Michelle Snider - A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the Grassmannian

dmtcs:2713 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2713
A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the GrassmannianArticle

Authors: Michelle Snider 1

We consider Buch's rule for K-theory of the Grassmannian, in the Schur multiplicity-free cases classified by Stembridge. Using a result of Knutson, one sees that Buch's coefficients are related to Möbius inversion. We give a direct combinatorial proof of this by considering the product expansion for Grassmannian Grothendieck polynomials. We end with an extension to the multiplicity-free cases of Thomas and Yong.

https://doi.org/10.46298/dmtcs.2713
Source: HAL:hal-01185405v1
Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Grassmannian,Richardson varieties,Grothendieck polynomials,Schur multiplicity free,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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