Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices
Abstract
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural properties of such lattices, with a particular focus on their rank structure, covering relations, and enumeration of elements per level. Leveraging these structural insights, we investigate necessary and sufficient conditions under which the lattice induced by a covering is isomorphic to classical geometric lattices, including the lattice of partitions, the lattice of subspaces of a vector space over a finite field, and the Dowling lattice. Our results provide a unified framework for comparing these combinatorial structures and contribute to the broader study of lattice theory, matroids, and their applications in combinatorics.
Keywords
Cite
@article{arxiv.2512.24569,
title = {Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices},
author = {Elvis Cabrera and Jyrko Correa},
journal= {arXiv preprint arXiv:2512.24569},
year = {2026}
}