论文标题
组合几何形状的奇异霍奇理论
Singular Hodge theory for combinatorial geometries
论文作者
论文摘要
我们介绍了矩阵的交叉点共同体学模块，并证明它满足了庞加莱二重性，硬左列施兹定理和霍奇 - 里曼的关系。作为应用，我们获得了Dowling和Wilson的最高猜想的证据，以及所有矩阵的Kazhdan-Lusztig多项式系数的非负性。
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applications, we obtain proofs of Dowling and Wilson's Top-Heavy conjecture and the nonnegativity of the coefficients of Kazhdan-Lusztig polynomials for all matroids.
