Non-Leaving-Face property for marked surfaces

簇代数的交换图具有不离开面性质

Exchange graphs of cluster algebras have the non-leaving-face property

本文证明了簇代数的交换图具有不离开面性质。

D型associahedra的直径与非离开面性质

The diameter of type D associahedra and the non-leaving-face property

本文证明D型associahedron的图直径为2n-2，并证明所有BCD型associahedra满足非离开面性质，同时给出反例说明该性质并非普遍成立。

The Face Structure and Geometry of Marked Order Polyhedra

We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand-Tsetlin polytopes and cones, as well as Berenstein-Zelevinsky polytopes, all of which have appeared in the representation theory of semi-simple Lie algebras. The faces of these polyhedra correspond to certain partitions of the underlying poset and we give a combinatorial characterization of these partitions. We specify a class of marked posets that give rise to polyhedra with facets in correspondence to the covering relations of the poset. On the convex geometrical side, we describe the recession…

关于标记序多面体的面数

On the number of faces of marked order polytopes

本文通过构造上链复形，将标记序多面体的 f-向量计算转化为上同调群维数计算，并给出其立方单纯剖分的纯组合描述。

A Continuous Family of Marked Poset Polytopes

For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of…

关于计数平面紧映射的拟多项式

On quasi-polynomials counting planar tight maps

本文利用平面映射的切片分解与双射方法，给出了计数具有指定面度数的平面紧映射的拟多项式显式公式，并将Tutte切片公式推广至所有非二分映射。