The lattice of closure relations of a poset

1994/09/17 by Michael Hawrylycz, Hawrylycz, Michael, Victor Reiner +1 · 1 citation
Computer Science · Decision Sciences · #06A07 #Advanced Algebra and Logic #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #FOS: Mathematics #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.math/9409218

openalex publication_date 1994/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

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• Convex Geometries via Hopf Monoids: Combinatorial Invariants, Reciprocity, and Supersolvability

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