Log-concavity of characteristic polynomials and the Bergman fan of matroids
Log-concavity of characteristic polynomials and the Bergman fan of matroids
复制标题
DOI：
10.1007/s00208-011-0777-6
复制
发表时间：
2012-11-01
影响因子：
1.4
通讯作者：
Katz, Eric
中科院分区：
文献类型：
--
作者：
Huh, June;Katz, Eric
在最近的一篇论文中，第一作者证明了在特征0领域可实现的特征性多项式系数的对数洞穴，并回答了图理论中读取的长期猜想。我们将证明扩展到所有可实现的矩阵，从而朝着更一般的rota-heron-welsh猜想。我们的证明是鉴于对降低的特征多项式的系数的识别，作为对复曲面品种特定相交问题的答案。然后，log-concavity遵循霍奇类型的不等式。
In a recent paper, the first author proved the log-concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0, answering a long-standing conjecture of Read in graph theory. We extend the proof to all realizable matroids, making progress towards a more general conjecture of Rota-Heron-Welsh. Our proof follows from an identification of the coefficients of the reduced characteristic polynomial as answers to particular intersection problems on a toric variety. The log-concavity then follows from an inequality of Hodge type.