Transversal Lattices
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2007
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909280664289280 |
|---|---|
| author | Bonin, Joseph E. |
| author_facet | Bonin, Joseph E. |
| contents | A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic flats are isomorphic to it are transversal. We investigate some sufficient conditions for a lattice to be a Tr-lattice; a corollary is that distributive lattices of dimension at most two are Tr-lattices. We give a necessary condition: each element in a Tr-lattice has at most two covers. We also give constructions that produce new Tr-lattices from known Tr-lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0702345 |
| institution | arXiv |
| publishDate | 2007 |
| record_format | arxiv |
| spellingShingle | Transversal Lattices Bonin, Joseph E. Combinatorics 05B35 A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic flats are isomorphic to it are transversal. We investigate some sufficient conditions for a lattice to be a Tr-lattice; a corollary is that distributive lattices of dimension at most two are Tr-lattices. We give a necessary condition: each element in a Tr-lattice has at most two covers. We also give constructions that produce new Tr-lattices from known Tr-lattices. |
| title | Transversal Lattices |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/math/0702345 |