The inverse Kazhdan-Lusztig polynomials of paving matroids are log-concave, proved via a new real-rootedness result for a Hadamard product with (1+t)^n.
On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid
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abstract
Following the work of Gao and Xie in [2], we state some properties of the inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers to a conjecture that states that regular connected matroids are non-degenerate. We link the degeneracy of a matroid to the inverse Kazhdan-Lusztig polynomial and we show that the Conjecture holds for modular matroids, by proving that degenerate modular matroids are not regular.
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Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids
The inverse Kazhdan-Lusztig polynomials of paving matroids are log-concave, proved via a new real-rootedness result for a Hadamard product with (1+t)^n.