SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 611-639, January 2020.
For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of the polytope for generic parameters.

中文翻译：

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连续的标记Poset多表位家族

SIAM离散数学杂志，第34卷，第1期，第611-639页，2020年1月。
对于任何带标记的坐姿，我们定义了一个连续的多面体族，用超立方体对它们进行参数化，概括了标记顺序和带标记的链多面体的概念。通过提供转移图，我们显示超立方体的顶点参数化了Ehrhart等效的多晶格族。当参数在超立方体的每个面的相对内部变化时，多面体的组合类型是恒定的。此外，借助于由与标记的姿态相关联的热带超平面布置引起的细分，我们给出了通用参数多面体顶点的明确描述。