Abstract
In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense of Edelman and Jamison [EJ]). We also characterize the modular elements of this lattice (when P has a greatest element) and compute its characteristic polynomial.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 301-310 |
| Number of pages | 10 |
| Journal | Algebra Universalis |
| Volume | 30 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1993 |