论文标题
面向仿期的矩形
Finitary affine oriented matroids
论文作者
论文摘要
我们在任意地面集的公理研究中启动了面向仿生的基型（AOM）的公理研究，从而获得了基本概念，例如未成年人，重新定位和自然嵌入到方向的矩阵复合物的框架中。对限制案例（FAOM）的限制使我们能够研究toper图和共证posets，并将FAOM视为定向的粉状半肌动物。我们展示了FAOMS的可壳性，并挑出与$ \ Mathbb {r}^n $相关同型的FAOM。最后，我们研究了对AOM的小组行动，在FAOM的情况下，其商是朝着仿生和复曲面伪拥齿理论的垫脚石。我们的结果包括半透明群体作用的多项式多项式的应用，将复曲率布置的枚举特性概括为综合定义的子序列的组合类别。这部分回答了Ehrenborg和Readdy的问题。
We initiate the axiomatic study of affine oriented matroids (AOMs) on arbitrary ground sets, obtaining fundamental notions such as minors, reorientations and a natural embedding into the frame work of Complexes of Oriented Matroids. The restriction to the finitary case (FAOMs) allows us to study tope graphs and covector posets, as well as to view FAOMs as oriented finitary semimatroids. We show shellability of FAOMs and single out the FAOMs that are affinely homeomorphic to $\mathbb{R}^n$. Finally, we study group actions on AOMs, whose quotients in the case of FAOMs are a stepping stone towards a general theory of affine and toric pseudoarrangements. Our results include applications of the multiplicity Tutte polynomial of group actions of semimatroids, generalizing enumerative properties of toric arrangements to a combinatorially defined class of arrangements of submanifolds. This answers partially a question by Ehrenborg and Readdy.
