Subdivisions of lower Eulerian posets
Combinatorics
2025-11-21 v1
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 -posets is given, as well as an application to computing the -index of an Eulerian poset. A companion paper explores applications to Kazhdan-Lusztig-Stanley theory.
Cite
@article{arxiv.2511.16608,
title = {Subdivisions of lower Eulerian posets},
author = {Alan Stapledon},
journal= {arXiv preprint arXiv:2511.16608},
year = {2025}
}