On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid.

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. Firstly, we show that the Conjecture holds for modular matroids, by proving that degenerate modular matroids are not regular; then, we also reduce the problem to proving that the statement holds on odd-rank matroids.