有理多面体的拟周期坍缩与GL_n（Z）-剪汇
Quasi-period collapse and GL_n(Z)-scissors congruence in rational polytopes
摘要：
当有理多胞形的Ehrhart拟多项式的拟周期小于该多胞形的分母时，发生拟周期坍缩。人们对这种现象知之甚少，所有已知的发生这种现象的案例都是用专门的方法证明的。本文给出了有理多面体中准周期坍缩的一个理论解释。我们表明，这种解释适用于文献中出现的一些以前的情况。我们还展示了有理多面体的Ehrhart多项式的例子，不是任何整数多面体的Ehrhart多项式。我们的方法依赖于仿射么模变换下的Ehrhart拟多项式的不变性。出于这个想法的相似性的剪刀全等问题，我们探讨了发展的Dehn一样的不变量的合理多面体的格设置。
英文摘要：
Quasi-period collapse occurs when the Ehrhart quasi-polynomial of a rational polytope has a quasi-period less than the denominator of that polytope. This phenomenon is poorly understood, and all known cases in which it occurs have been proven with ad hoc methods. In this note, we present a conjectural explanation for quasi-period collapse in rational polytopes. We show that this explanation applies to some previous cases appearing in the literature. We also exhibit examples of Ehrhart polynomials of rational polytopes that are not the Ehrhart polynomials of any integral polytope. Our approach depends on the invariance of the Ehrhart quasi-polynomial under the action of affine unimodular transformations. Motivated by the similarity of this idea to the scissors congruence problem, we explore the development of a Dehn-like invariant for rational polytopes in the lattice setting.
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