Year: 2026
Type: preprint
Abstract: In this paper we study whether there is a global to local principle for the homology of order complexes of finite lattices. We explore whether the non-vanishing of the homology of a lattice in degree $a+b-2$ forces the existence of a pair of lattice-complements whose open intervals below have non-vanishing homology in degrees $a$ and $b$ respectively. We consider the same question also in the language of multigraded free resolutions. We provide positive evidence for the existence of such pairs and give counterexamples to strengthenings of the question.
Source: arXiv (Cornell University)
Authors: Faridi, Sara, Veer, Dharm, Welker, Volkmar
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214127023