The lattice of closure relations of a poset

Details The lattice of closure relations of a poset The lattice of closure relations of a poset

1994-09-17

arxiv.org/abs/math/9409218v1

Mathematics

Combinatorics

8 pages

Scientific paper

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). We also characterize the modular elements
of this lattice and compute its characteristic polynomial.

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