格正方体、立方体和超立方体的Ehrhart多项式
Ehrhart polynomial for lattice squares, cubes and hypercubes
摘要：
本文用$d\in \{2,3,4\}$在$\mathbb R^d$中构造整数格正方形、正方形和超正方形。对于正方形和立方体，我们找到一个完整的描述他们的Ehrhart多项式。对于超立方体，我们计算了其中一个系数，并证明了其他两个未知系数之间存在简单的线性关系。这允许作为制定一个猜想是什么Ehrhart多项式在这种情况下。
英文摘要：
In this paper we are constructing integer lattice squares, cubes or hypercubes in $\mathbb R^d$ with $d\in \{2,3,4\}$. For squares and cubes we find a complete description of their Ehrhart polynomial. For hypercubes, we compute one of the coefficients and show that there exists a simple linear relation between the other two unknown coefficients. This allows as to formulate a conjecture of what the Ehrhart polynomial is in this case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
