2022/07/10 by Gunnar Fløystad, Fløystad, Gunnar
Computer Science · Mathematics · #05C05 05C69 #05E45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2207.04444
openalex publication_date 2022/07/10 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28
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 ≥ s and vertex partitions whose parts have minimal distance ≥ s+1. A consequence is results on partitions of natural numbers, where the parts have minimal bounds on spacing.