2004/09/14 by Eva Maria Feichtner, Eva María Feichtner, Feichtner, Eva Maria · 2 citations
Computer Science · Mathematics · #05E25 #57Q05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05E25 #msc:57Q05
paper · pdf · doi:10.48550/arxiv.math/0409235
13 pages, 5 figures; minor revision, references updated, to appear in Pacific J. Math
openalex publication_date 2004/09/14 · arxiv created 2005/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit an identity of abstract simplicial complexes between the well-studied complex of trees and the reduced minimal nested set complex of the partition lattice. We conclude that the order complex of the partition lattice can be obtained from the complex of trees by a sequence of stellar subdivisions. We provide an explicit cohomology basis for the complex of trees that emerges naturally from this context. Motivated by these results, we review the generalization of complexes of trees to complexes of k-trees by Hanlon, and we propose yet another, in the context of nested set complexes more natural, generalization.