An Ehrhart Series Formula For Reflexive Polytopes
An Ehrhart Series Formula For Reflexive Polytopes
复制标题
自反多面体的埃尔哈特级数公式
DOI：
10.37236/1153
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Benjamin Braun
中科院分区：
文献类型：
--
作者：
Benjamin Braun
众所周知，对于$P$和$Q$晶格多胞体，$P\times Q$的Ehrhart多项式满足$L_{P\times Q}(t)=L_P(t)L_Q(t)$。我们证明，$P$、$Q$ 和自由和 $P\oplus Q$ 的 Ehrhart 级数之间存在类似的乘法关系，当 $P$ 自反且 $Q$ 内部包含 $0$ 时，该关系成立。
It is well known that for $P$ and $Q$ lattice polytopes, the Ehrhart polynomial of $P\times Q$ satisfies $L_{P\times Q}(t)=L_P(t)L_Q(t)$. We show that there is a similar multiplicative relationship between the Ehrhart series for $P$, for $Q$, and for the free sum $P\oplus Q$ that holds when $P$ is reflexive and $Q$ contains $0$ in its interior.