论文标题
多变量卷，ehrhart和$ h^*$ - 多项式多项式
Multivariate volume, Ehrhart, and $h^*$-polynomials of polytropes
论文作者
论文摘要
已广泛研究了单变量的ehrhart和$ h^*$ - 晶格多型的多项式。我们描述了从曲折的几何形状计算晶格多型晶格多项式的多元版本的多元版本的方法，这些版本既热态和经典凸面。这些算法应用于尺寸为2,3和4的所有多层，产生了大量的整数多项式。我们对基本多层的常规中央细分的定期中央细分进行了完整的组合描述。最后，我们在维度4中提供了类似系数的部分表征。
The univariate Ehrhart and $h^*$-polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, Ehrhart and $h^*$-polynomials of lattice polytropes, which are both tropically and classically convex. These algorithms are applied to all polytropes of dimensions 2,3 and 4, yielding a large class of integer polynomials. We give a complete combinatorial description of the coefficients of volume polynomials of 3-dimensional polytropes in terms of regular central subdivisions of the fundamental polytope. Finally, we provide a partial characterization of the analogous coefficients in dimension 4.
