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arXiv · 2512.24569

Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices

Elvis Cabrera·Jyrko Correa
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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.

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Elvis Cabrera, Jyrko Correa. 2025-12-31. Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices. https://arxiv.org/abs/2512.24569

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