论文标题
部分置换和交替的符号矩阵多面体
Partial permutation and alternating sign matrix polytopes
论文作者
论文摘要
我们定义并研究了一个新的多型家族，这些家族形成是部分交替符号矩阵的凸壳。我们确定这些多面体的不平等描述，小平面的数量和面部晶格。我们还研究了作为这些多面体的投影自然出现的部分置换。我们列举了面部，并以布尔晶格中的链条来表征部分置换的面部晶格。最后，当一个参数固定为两个时，我们对部分置换螺旋体的体积有一个结果和猜想。
We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial permutohedra that we show arise naturally as projections of these polytopes. We enumerate facets and also characterize the face lattices of partial permutohedra in terms of chains in the Boolean lattice. Finally, we have a result and a conjecture on the volume of partial permutohedra when one parameter is fixed to be two.
