论文标题
多面有阶的阶段对称对称性的多面有的ehrhart理论
The equivariant Ehrhart theory of polytopes with order-two symmetries
论文作者
论文摘要
我们研究了在该组的非平凡作用下以二的阶段的非平凡作用，多型族群的ehrhart理论是不变的。我们研究了多面体的多型家族，其多项式的多项式既成功又无法有效，尤其是循环的对称边缘多型和合理的跨多个物体。如果要求多层顶点具有积分坐标以允许有理坐标，则后者对有效性的猜想提供了反例。此外，我们展示了这样的反例，其Ehrhart功能具有一度周期，并且与晶格多层的Ehrhart函数一致。
We study the equivariant Ehrhart theory of families of polytopes that are invariant under a non-trivial action of the group with order two. We study families of polytopes whose equivariant $H^*$-polynomial both succeed and fail to be effective, in particular, the symmetric edge polytopes of cycles and the rational cross-polytope. The latter provides a counterexample to the effectiveness conjecture if the requirement that the vertices of the polytope have integral coordinates is loosened to allow rational coordinates. Moreover, we exhibit such a counterexample whose Ehrhart function has period one and coincides with the Ehrhart function of a lattice polytope.
