树与堆叠单纯复形中顶点和面的划分
Partitons of vertices and facets in trees and stacked simplicial complexes
AI总结：
本文为堆叠单纯复形（含树、多边形三角剖分、堆叠多面体）建立了面划分与顶点独立集划分之间的显式双射，并将其推广到带最小距离约束的情形，进而导出自然数划分的间距下界结果。
摘要：
对于堆叠单纯复形（其特殊子类包括：树、多边形的三角剖分、堆叠多面体），我们给出了面的划分（对于树：边的划分）与顶点划分为独立集之间的显式双射。更一般地，我们给出了部分之间最小距离≥s的面划分与部分之间最小距离≥s+1的顶点划分之间的双射。其一个推论是关于自然数划分的结果，其中各部分在间距上具有最小下界。
英文摘要：
For stacked simplicial complexes, (special subclasses of such are: trees, triangulations of polygons, stacked polytopes), we give an explicit bijection between partitions of facets (for trees: edges), and partitions of vertices into independent sets. More generally we give bijections between facet partitions whose parts have minimal distance $\geq s$ and vertex partitions whose parts have minimal distance $\geq s+1$. A consequence is results on partitions of natural numbers, where the parts have minimal bounds on spacing.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
