Line Shellings of Geometric Lattices
Combinatorics
2026-01-09 v1
Abstract
Inspired by Bruggesser-Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid induced by a building set, we show that the lexicographic order of the coordinates of its vertices is a shelling order. This gives a new proof of Bj\"orner's classical result that the order complex of the lattice of flats of a matroid is shellable, and demonstrates shellability for all nested set complexes for matroids.
Keywords
Cite
@article{arxiv.2601.05119,
title = {Line Shellings of Geometric Lattices},
author = {Spencer Backman and Galen Dorpalen-Barry and Anastasia Nathanson and Ethan Partida and Noah Prime},
journal= {arXiv preprint arXiv:2601.05119},
year = {2026}
}
Comments
33 pages. Comments welcome!