The lattice of closure relations on a poset

Michael Hawrylycz, Victor Reiner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)301-310
Number of pages10
JournalAlgebra Universalis
Volume30
Issue number3
DOIs
StatePublished - Sep 1993

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