论文标题
关于图意理想的强大鲁棒性特性
On the strongly robustness property of toric ideals
论文作者
论文摘要
对于每个复合理想，一个人都可以将定向的矩形结构与图形和另一个曲折的理想组成，称为花束理想。该图的连接组件称为花束。花束有三种类型；免费，混合和非混合。我们证明，以下集合的基数 - 必不可少的元素，最小的马尔可夫基地，通用马尔可夫基础和圆环理想的通用gröbner基础 - 仅取决于花束的类型和花束理想的类型。这些结果使我们能够引入强大的鲁棒性简单复合物，并表明它决定了强大的鲁棒性。对于Codimension 2曲折的理想，我们研究了强大的鲁棒性简单复合物，并证明了鲁棒性意味着强大的鲁棒性。
To every toric ideal one can associate an oriented matroid structure, consisting of a graph and another toric ideal, called bouquet ideal. The connected components of this graph are called bouquets. Bouquets are of three types; free, mixed and non mixed. We prove that the cardinality of the following sets - the set of indispensable elements, minimal Markov bases, the Universal Markov basis and the Universal Gröbner basis of a toric ideal - depends only on the type of the bouquets and the bouquet ideal. These results enable us to introduce the strongly robustness simplicial complex and show that it determines the strongly robustness property. For codimension 2 toric ideals, we study the strongly robustness simplicial complex and prove that robustness implies strongly robustness.
