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A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids
Abstract
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 for uniform matroids, our formula has a nice combinatorial interpretation.
Subject Area
Mathematics
Recommended Citation
Nasr, George David, "A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids" (2021). ETD collection for University of Nebraska-Lincoln. AAI28712831.
https://digitalcommons.unl.edu/dissertations/AAI28712831