Some algebra and combinatorics of matroid Kazhdan-Lusztig polynomials
speaker: Max Wakefield (United States Naval Academy, Annapolis)abstract: The Kazhdan-Lusztig polynomial of a matroid is a combinatorial invariant which computes the intersection cohomology of the reciprocal plane if the matroid is representable over some field. There are many unknown properties about this polynomial. For example, it is conjectured that the coefficients are non-negative for all matroids. In this talk we will briefly review how these polynomials are similar to the classical Kazhdan-Lusztig polynomials. Then we will discuss a combinatorial formula for their coefficients in terms of flags in the matroids lattice of flats. This formula is given by sums of ``top-heavy'' pairs of flag Whitney numbers of the second kind and we will note the recent result of Huh and Wang on the top-heavy conjecture.
timetable:
Tue 6 Jun, 15:30 - 16:10, Aula Dini
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