论文标题
双甲体
The bipermutahedron
论文作者
论文摘要
谐波多层人和双甲体是两个相关的多型，它们在Ardila，Denham和Huh在Matroids的Lagrangian几何学上的作品中出现。我们研究双甲体。我们表明，它的面孔与没有孤立的顶点的顶点标记和边缘标记的多编码进行了两次射击。其F-vector的生成函数是对三个变量Rogers-Ramanujan函数的简单评估。 我们表明，双甲状腺扇的H-多项式是Bieulerian多项式，它根据双纤维的下降数量进行计数。我们构建了n个三角形的乘积的单型三角剖分，该乘积在组合上等同于（三重锥）的第ntipermutahedral Fan。然后，Ehrhart理论为我们提供了Bieulerian多项式的公式，我们用来表明该多项式是实地的，并且双甲状腺扇形的H-vector是对数conconcove and Unimopal。 我们描述了双甲体的所有变形；也就是说，双毛皮的圆环品种的丰富锥体。我们证明，在这个家族的所有多面体中，双摩特族人具有最大的对称组。最后，我们证明了双甲基体和谐波多层的Minkowski商等于2。
The harmonic polytope and the bipermutahedron are two related polytopes which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We study the bipermutahedron. We show that its faces are in bijection with the vertex-labeled and edge-labeled multigraphs with no isolated vertices; the generating function for its f-vector is a simple evaluation of the three variable Rogers--Ramanujan function. We show that the h-polynomial of the bipermutahedral fan is the biEulerian polynomial, which counts bipermutations according to their number of descents. We construct a unimodular triangulation of the product of n triangles that is combinatorially equivalent to (the triple cone over) the nth bipermutahedral fan. Ehrhart theory then gives us a formula for the biEulerian polynomial, which we use to show that this polynomial is real-rooted and that the h-vector of the bipermutahedral fan is log-concave and unimodal. We describe all the deformations of the bipermutahedron; that is, the ample cone of the bipermutahedral toric variety. We prove that among all polytopes in this family, the bipermutahedron has the largest possible symmetry group. Finally, we show that the Minkowski quotient of the bipermutahedron and the harmonic polytope equals 2.
