论文标题
谐波多层
The harmonic polytope
论文作者
论文摘要
我们研究了在Ardila，Denham和Huh在Matroid的拉格朗日几何学上的作品中出现的谐波多层。我们描述了它的组合结构，表明它是$（2n-2）$ - 尺寸多层，带有$（n！）^2（1+ \ frac12+\ cdots+\ frac1n）$ Vertices和$ 3^n-3 $ facets。我们还为其体积提供了一个公式：它是所有$ n $ edges的连接二分子图的紫色理想的投射品种的加权总和；或等效地，所有相应的概括性定位的晶格点计数的加权总和。
We study the harmonic polytope, which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We describe its combinatorial structure, showing that it is a $(2n-2)$-dimensional polytope with $(n!)^2(1+\frac12+\cdots+\frac1n)$ vertices and $3^n-3$ facets. We also give a formula for its volume: it is a weighted sum of the degrees of the projective varieties of all the toric ideals of connected bipartite graphs with $n$ edges; or equivalently, a weighted sum of the lattice point counts of all the corresponding trimmed generalized permutahedra.
