Subdivisions of lower Eulerian posets

2025/11/20 by Alan Stapledon, Stapledon, Alan
Computer Science · Mathematics · #06A07 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.16608

openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

There is a natural notion of a subdivision of a lower Eulerian poset called a strong formal subdivision, which abstracts the notion of a polyhedral subdivision of a polytope, or a proper, surjective morphism of fans. We show that there is a canonical bijection between strong formal subdivisions and triples consisting of a lower Eulerian poset, a corresponding rank function, and a non-minimal element such that the join with any other element exists. The bijection uses the non-Hausdorff mapping cylinder construction introduced by Barmak and Minian. A corresponding bijection for CW-posets is given, as well as an application to computing the cd-index of an Eulerian poset. A companion paper explores applications to Kazhdan-Lusztig-Stanley theory.

Citations

• Chow functions for partially ordered sets
• The local motivic monodromy conjecture for simplicial nondegenerate singularities
• Poset subdivisions and the mixed cd-index
• The cd-Index: A Survey
• The cylinder of a relation and generalized versions of the Nerve Theorem
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• On Quillen's Theorem A for posets
• Decomposition theorem for the cd-index of Gorenstein* posets
• Simple Homotopy Types and Finite Spaces
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Related

• Subdivisions of lower Eulerian posets and KLS theory
• Poset subdivisions and the mixed cd-index
• Subdividing the cd-index of Eulerian Posets
• Lattice Minors and Eulerian Posets
• CW posets after the Poincare Conjecture