Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24569 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911347562774528 |
|---|---|
| author | Cabrera, Elvis Correa, Jyrko |
| author_facet | Cabrera, Elvis Correa, Jyrko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices Cabrera, Elvis Correa, Jyrko Combinatorics 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. |
| title | Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.24569 |