A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids

We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan-Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. We also show the positivity of these coeffic...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2021-12, Vol.28 (4)
Main Authors: Lee, Kyungyong, George D. Nasr, Radcliffe, Jamie
Format: Article
Language:English
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Summary:We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan-Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. We also show the positivity of these coefficients using our formula. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation.
ISSN:1077-8926
1077-8926
DOI:10.37236/10602