论文标题
具有任意期Ehrhart系数的理性多面体
Rational polytopes with Ehrhart coefficients of arbitrary period
论文作者
论文摘要
E. ehrhart的开创性结果指出，通过正整数$ k $扩张的整数晶格点的数量是$ k $ ----即“ polynomial”的准整数$ k $，即系数本身是$ k $的“多项式”。利用F. liu的结果对环状多面体的ehrhart多项式，我们构建了任意维度的不必要的符合理性的多面体，其中在ehrhart quasi-polynomial中出现的系数函数周期出现了任意值。
A seminal result of E. Ehrhart states that the number of integer lattice points in the dilation of a rational polytope by a positive integer $k$ is a quasi-polynomial function of $k$ --- that is, a "polynomial" in which the coefficients are themselves periodic functions of $k$. Using a result of F. Liu on the Ehrhart polynomials of cyclic polytopes, we construct not-necessarily-convex rational polytopes of arbitrary dimension in which the periods of the coefficient functions appearing in the Ehrhart quasi-polynomial take on arbitrary values.
