论文标题
计算线条质质细胞，其边界和交叉点
Computing positroid cells in the Grassmannian of lines, their boundaries and their intersections
论文作者
论文摘要
阳性是尼科夫（Postnikov）在非阴性司法研究中引入的成曲子家族。尤其是，阳性质体列举了完全非负grassmannian的CW分解。此外，后尼科夫已经确定了具有阳性型阳性物体的几个组合物体家族。我们将在某些图中为Gr $ _ {\ geq 0}（2，n）$的正源性构成正质体的另一个表征。我们使用此表征来计算阳性细胞的维度和边界。这也导致对阳性细胞交集的组合描述，这很容易计算。我们的技术依赖于确定$ \ {1，\ ldots，n \} $的子集的不同方法来表示阳性的依赖集，即具有非负性最大矿工的矩阵列之间的依赖项。此外，我们提供了一种算法来计算集合中包含的所有最大效果。
Positroids are families of matroids introduced by Postnikov in the study of non-negative Grassmannians. In particular, positroids enumerate a CW decomposition of the totally non-negative Grassmannian. Furthermore, Postnikov has identified several families of combinatorial objects in bijections with positroids. We will provide yet another characterization of positroids for Gr$_{\geq 0}(2,n)$, the Grassmannians of lines, in terms of certain graphs. We use this characterization to compute the dimension and the boundary of positroid cells. This also leads to a combinatorial description of the intersection of positroid cells, that is easily computable. Our techniques rely on determining different ways to enlarge a given collection of subsets of $\{1,\ldots,n\}$ to represent the dependent sets of a positroid, that is the dependencies among the columns of a matrix with non-negative maximal minors. Furthermore, we provide an algorithm to compute all the maximal positroids contained in a set.
