Geodesic
A flag Whitney number formula for matroid Kazhdan-Lusztig polynomials
Max Wakefield1
1US Naval Academy
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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For a representation of a matroid the combinatorially defined Kazhdan-Lusztig polynomial computes the intersection cohomology of the associated reciprocal plane. However, these polynomials are difficult to compute and there are numerous open conjectures about their structure. For example, it is unknown whether or not the coefficients are non-negative for non-representable matroids. The main result in this note is a combinatorial formula for the coefficients of these matroid Kazhdan-Lusztig polynomials in terms of flag Whitney numbers. This formula gives insight into some vanishing behavior of the matroid Kazhdan-Lusztig polynomials.
DOI : 10.37236/6120
Classification : 05B35, 52B40, 06A07, 11B75
Mots-clés : matroid, Kazhdan-Lusztig polynomial, incidence algebra, characteristic polynomial, poset

Max Wakefield  1

1 US Naval Academy 
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Max Wakefield. A flag Whitney number formula for matroid Kazhdan-Lusztig polynomials. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6120

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