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) |
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Pages (from-to) | 301-310 |
Number of pages | 10 |
Journal | Algebra Universalis |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1993 |