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Parallel translates of represented matroids
Advances in Applied Mathematics ( IF 1.0 ) Pub Date : 2021-02-25 , DOI: 10.1016/j.aam.2021.102176
Beifang Chen , Houshan Fu , Suijie Wang

Given an F-represented matroid (M,ρ) with the ground set [m], the representation ρ naturally defines a hyperplane arrangement Aρ. We will study its parallel translates Aρ,g of Aρ for all gFm. Its intersection semi-lattices L(Aρ,g) and the characteristic polynomials χ(Aρ,g,t) will be classified by the intersection lattice of the derived arrangement Aδρ, which is a hyperplane arrangement associated with the derived matroid (δM,δρ) and also known as the discriminantal arrangement in the literature. As a byproduct, we obtain a comparison result and a decomposition formula on the characteristic polynomials χ(Aρ,g,t).



中文翻译:

代表拟阵的平行翻译

给定一个 F代表的拟阵 中号ρ 与地面设置 [],表示ρ自然定义了超平面排列一种ρ。我们将研究其平行翻译一种ρG一种ρ 对所有人 GF。它的交点半格大号一种ρG 和特征多项式 χ一种ρGŤ 将根据派生排列的相交格子进行分类 一种δρ,这是与派生的拟阵相关的超平面布置 δ中号δρ并且在文献中也称为判别式排列。作为副产品,我们获得了特征多项式的比较结果和分解公式χ一种ρGŤ

更新日期:2021-02-26
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