论文标题
2度的晶格编排
Lattice zonotopes of degree 2
论文作者
论文摘要
Ehrhart多项式$ ehr_p（n）$ of lattice polytope $ p $提供了所有整数$ n \ n \ geq 0 $的$ n $ th膨胀$ p $中的整数晶格点的数量。 $ p $的程度定义为其$ h^\ ast $ - 多项式的程度，这是Ehrhart多项式的特殊转换，具有许多有用的属性，是Ehrhart理论中分类问题的重要工具。地位是线段的Minkowski（点式）总和。我们对晶格编织度的所有ehrhart多项式分类为$ 2 $ $ 2 $，从而补充了Scott（1976），Treutlein（2010）和Henk-Tagami（2009）的结果。我们的证明是建设性的：考虑一下固体角度和晶格宽度，我们提供了所有$ 3 $维度的$ 2 $ 2 $的表征。
The Ehrhart polynomial $ehr_P (n)$ of a lattice polytope $P$ gives the number of integer lattice points in the $n$-th dilate of $P$ for all integers $n\geq 0$. The degree of $P$ is defined as the degree of its $h^\ast$-polynomial, a particular transformation of the Ehrhart polynomial with many useful properties which serves as an important tool for classification questions in Ehrhart theory. A zonotope is the Minkowski (pointwise) sum of line segments. We classify all Ehrhart polynomials of lattice zonotopes of degree $2$ thereby complementing results of Scott (1976), Treutlein (2010), and Henk-Tagami (2009). Our proof is constructive: by considering solid-angles and the lattice width, we provide a characterization of all $3$-dimensional zonotopes of degree $2$.
