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arXiv · 2006.10209

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

Kyungyong Lee·George D. Nasr·Jamie Radcliffe
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Abstract

We prove the positivity of Kazhdan-Lusztig polynomials for sparse paving matroids, which are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. The positivity follows from a remarkably simple combinatorial formula we discovered for these polynomials using skew young tableaux. This supports the conjecture that Kazhdan-Lusztig polynomials for all matroids have non-negative coeffiecients. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation.

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Kyungyong Lee, George D. Nasr, Jamie Radcliffe. 2020-06-18. A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids. https://arxiv.org/abs/2006.10209

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