论文标题
ehrhart $ h^*$ - 多项式多项式的分解
Decompositions of Ehrhart $h^*$-polynomials for rational polytopes
论文作者
论文摘要
ehrhart pytope $ p $的ehrhart quasipolyNomial编码$ p $的整数晶格点的数量，而$ h^*$ - $ p $的$ h^*$ - poy-p $是随附的生成功能的分子。我们为$ H^*$ - 多项式的多项式提供了两个分解公式。第一个分解概括了Betke和McMullen的定理，用于晶格多面体。我们使用理性的betke--mcmullen公式为$ h^*$ - 理性多元化的多项式提供了斯坦利单调定理的新颖证明。第二个分解概括了Stapledon的结果，我们用来提供了斯坦利和hibi不平等的合理扩展，该系数是$ h^*$ - 多项式用于晶格多面体的系数。最后，我们将结果应用于包含二元组为晶格多塔的原点的有理多面体。
The Ehrhart quasipolynomial of a rational polytope $P$ encodes the number of integer lattice points in dilates of $P$, and the $h^*$-polynomial of $P$ is the numerator of the accompanying generating function. We provide two decomposition formulas for the $h^*$-polynomial of a rational polytope. The first decomposition generalizes a theorem of Betke and McMullen for lattice polytopes. We use our rational Betke--McMullen formula to provide a novel proof of Stanley's Monotonicity Theorem for the $h^*$-polynomial of a rational polytope. The second decomposition generalizes a result of Stapledon, which we use to provide rational extensions of the Stanley and Hibi inequalities satisfied by the coefficients of the $h^*$-polynomial for lattice polytopes. Lastly, we apply our results to rational polytopes containing the origin whose duals are lattice polytopes.
