f-Vectors of Triangulated Balls

来自三角剖分曲面的$g$-向量锥的密度

Density of $g$-vector cones from triangulated surfaces

本文研究了标记曲面定义的簇代数的$g$-向量锥，利用格结构和剪切坐标确定了其并集闭包，并据此证明了相应簇范畴中簇倾斜对象交换图的连通性。

f-vectors of Simplicial Posets that are Balls

Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-vectors. These results allow us to give a complete characterization of the h-vectors of simplicial poset balls up through dimension six.

A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Integers

A combinatorial problem that came up in Combinatorial Chemistry is solved.

h-Vectors of simplicial cell balls

A simplicial cell ball is a simplicial poset whose geometric realization is homeomorphic to a ball. Recently, Samuel Kolins gave a series of necessary conditions and sufficient conditions on $h$-vectors of simplicial cell balls, and characterized them up to dimension 6. In this paper, we extend Kolins' results. We characterize all possible $h$-vectors of simplicial cell balls in arbitrary dimension.

Genocchi Numbers and f-Vectors of Simplicial Balls

The Genocchi numbers are the coefficients of the generating function 2t/(e^t+1). In this note we will give an equation for simplicial balls which involves this numbers. It relates the number of faces in the interior of the ball with the number of faces in the boundary of the ball. This is a variation of similar equations given in [McMullen 2004] and [Herrmann and Joswig 2006].

Intersecting families of extended balls in the Hamming spaces

A family $\mathcal{F}$ of subsets of a set $X$ is $t$-intersecting if $\vert A_i \cap A_j \vert \geq t$ for every $A_i, \; A_j \in \mathcal{F}$. We study intersecting families in the Hamming geometry. Given $X=\mathbb{F}_q^3$ a vector space over the finite field $\mathbb{F}_q$, consider a family where each $A_i$ is an extended ball, that is, $A_i$ is the union of all balls centered in the scalar multiples of a vector. The geometric behavior of extended balls is discussed. As the main result, we investigate a ``large" arrangement of vectors whose extended balls are ``highly intersecting". Consi…

图上的二阶微分算子

Second Order Differential Operators on Graphs

研究图上二阶微分算子，通过探究半径为二的球的几何结构及相关自然满射，得出二阶微分算子的标准型、伴随公式及换位子为向量场的充要条件等结论。

The complex plank problem, revisited

Ball's complex plank theorem states that if $v_1,\dots,v_n$ are unit vectors in $\mathbb{C}^d$, and $t_1,\dots,t_n$, non-negative numbers satisfying $\sum_{k=1}^nt_k^2 = 1,$ then there exists a unit vector $v$ in $\mathbb{C}^d$ for which $|\langle v_k,v \rangle | \geq t_k$ for every $k$. Here we present a streamlined version of Ball's original proof.