矩阵 h 向量和混合欧拉数的对数凹性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2020-05-05 DOI:10.1215/00127094-2023-0021

A. Berget, Hunter Spink, Dennis Tseng

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引用次数: 18

摘要

对于任意矩阵 $M$，我们利用由格拉斯曼产生的组合周环 $A^\bullet(M)$ 中某些同义类的混合交集数来计算图特多项式 $T_M(x,y)$。利用混合霍奇-黎曼关系，我们推导出了母题复数的 h 向量的对数凹性的加强，改进了道森的一个古老猜想，阿迪拉、德纳姆和胡最近公布了该猜想的证明。

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Log-concavity of matroid h-vectors and mixed Eulerian numbers

For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain tautological classes in the combinatorial Chow ring $A^\bullet(M)$ arising from Grassmannians. Using mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the h-vector of a matroid complex, improving on an old conjecture of Dawson whose proof was announced recently by Ardila, Denham and Huh.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.