A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the Grassmannian
Michelle Snider
TL;DR
This paper provides a combinatorial proof linking Buch's K-theory coefficients for Grassmannian Schur multiplicity-free cases to Moebius inversion, extending results to Thomas and Yong's cases.
Contribution
It introduces a direct combinatorial proof connecting Buch's coefficients with Moebius inversion and extends the classification to additional multiplicity-free cases.
Findings
Buch's coefficients relate to Moebius inversion in Schur multiplicity-free cases.
A combinatorial proof for the product expansion of Grassmannian Grothendieck polynomials.
Extension of results to Thomas and Yong's multiplicity-free cases.
Abstract
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 Moebius 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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry