Complementary vectors of simplicial complexes
Combinatorics
2025-04-30 v1 Commutative Algebra
Abstract
We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley-Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes.
Cite
@article{arxiv.2504.20264,
title = {Complementary vectors of simplicial complexes},
author = {Matt Larson and Alan Stapledon},
journal= {arXiv preprint arXiv:2504.20264},
year = {2025}
}
Comments
16 pages