论文标题
双孔多型和热带线性空间
Biconvex Polytopes and Tropical Linear Spaces
论文作者
论文摘要
Biconvex polytope是有限多点的经典和热带凸壳。给定比科结构多色，对于它的每个顶点，我们构建了一个有向的bigraph和gammoid，以便这些γ-胶体的基础多型的集合是催眠术的成矩形细分，从而证明了一个biconvex biConvex多型，以热带线性空间的一个细胞出现。我们的构造提供了手动可行的指南，以将hypersimplex细化为基础多面体，而无需诉诸计算机。我们将排名4的案例作为演示。我们还表明，从任何（K-1）二维双杆的顶点注入了k不确定的（k-1）单元。
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid so that the collection of base polytopes of those gammoids is a matroid subdivision of the hypersimplex, thereby proving a biconvex polytope arises as a cell of a tropical linear space. Our construction provides manually feasible guidelines for subdividing the hypersimplex into base polytopes, without resorting to computers. We work out the rank-4 case as a demonstration. We also show there is an injection from the vertices of any (k-1)-dimensional biconvex polytope into the degree-(k-1) monomials in k indeterminates.
