Order, lattices, ordered algebraic structures Modular and complemented lattices Concept
Geometric lattice
Summary
A geometric lattice is a finite lattice that is atomistic and semimodular. These lattices are exactly the lattices of flats of finite matroids. So they give an order-theoretic description of matroids, in which the atoms are the points and the rank function measures dimension. Lattices of subspaces of a finite vector space, Boolean lattices of subsets of a finite set and lattices of partitions are geometric.
Further reading
About this page
| Tag | VDF7CGPC0P |
|---|---|
| URI | m2://VDF7CGPC0P |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06C10, 05B35 |
| Specializes | Semimodular lattice |
| Same as |
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