论文标题
大类矩阵的估值不变性
Valuative invariants for large classes of matroids
论文作者
论文摘要
我们研究了曲霉理论中的操作，该操作允许一个人通过放松\ emph {parcented subset}将给定的矩阵转变为另一个碱基。该框架提供了一类拆分矩阵的新组合表征。此外，它允许描述Hypersimplex的显式矩阵细分，进而可以用来写下混凝土公式，以评估这些矩阵上任何不变的评估。这表明对分裂矩阵的评估仅取决于不变的舒伯特矩阵的可行亚类的行为。我们系统地解决了几个不变的方法的后果。它们包括基础多型的体积和ehrhart多项式，Tutte多项式，Kazhdan-lusztig多项式，第一类和第二类的惠特尼数字，Spectrum spectrum多项式以及denham，denham，由链，链的polynomials and spymials and speyer's $ g $ -poly-polynommials，以及以及均等的，以及以及以及均等的chow ros and ass chow ros and ass chow。希尔伯特 - 辉煌系列。这种设置的灵活性使我们能够为列出的不变式提供统一的解释；此外，我们强调它是一种强大的计算工具，可以生成明确的数据和具体示例。
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a new combinatorial characterization of the class of split matroids. Moreover, it permits to describe an explicit matroid subdivision of a hypersimplex, which in turn can be used to write down concrete formulas for the evaluations of any valuative invariant on these matroids. This shows that evaluations on split matroids depend solely on the behavior of the invariant on tractable subclass of Schubert matroids. We address systematically the consequences of our approach for several invariants. They include the volume and Ehrhart polynomial of base polytopes, the Tutte polynomial, Kazhdan--Lusztig polynomials, the Whitney numbers of the first and second kind, spectrum polynomials and a generalization of these by Denham, chain polynomials and Speyer's $g$-polynomials, as well as Chow rings of matroids and their Hilbert--Poincaré series. The flexibility of this setting allows us to give a unified explanation for several recent results regarding the listed invariants; furthermore, we emphasize it as a powerful computational tool to produce explicit data and concrete examples.
