拟阵的星面体几何

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Christopher Eur, June Huh, Matt Larson
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引用次数: 18

摘要

摘要利用星面体环变体的几何特性来研究拟阵。我们用星面体环的上同环确定了拟阵的赋值群,并证明了拟阵的赋值、同调和数值等价关系是重合的。我们建立了矩阵的Tutte多项式的一个新的对数凹性结果,回答了关于Postnikov-Shapiro代数的Wagner和Shapiro-Smirnov-Vaintrob问题,并计算了矩阵Schubert单元的chen - schwartz - macpherson类。中心结构是“增广的同义类阵”,在星面体上的某些环矢量束的基础上建模。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stellahedral geometry of matroids
Abstract We use the geometry of the stellahedral toric variety to study matroids. We identify the valuative group of matroids with the cohomology ring of the stellahedral toric variety and show that valuative, homological and numerical equivalence relations for matroids coincide. We establish a new log-concavity result for the Tutte polynomial of a matroid, answering a question of Wagner and Shapiro–Smirnov–Vaintrob on Postnikov–Shapiro algebras, and calculate the Chern–Schwartz–MacPherson classes of matroid Schubert cells. The central construction is the ‘augmented tautological classes of matroids’, modeled after certain toric vector bundles on the stellahedral toric variety.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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