Düvelmeyer, Nico ; Wenzel, Walter : A Characterization of Ordered Sets and Lattices via Betweenness Relations

Author(s):

Düvelmeyer, Nico
Wenzel, Walter

Title:

A Characterization of Ordered Sets and Lattices via Betweenness Relations

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 3, 2003

Mathematics Subject Classification:

06A06			[ Partial order, general ]
06A07			[ Combinatorics of partially ordered sets ]
06A15			[ Galois correspondences, closure operators ]
06B05			[ Structure theory ]
06B20			[ Varieties of lattices ]

Abstract:

For a set X with at least 3 elements, we prove a canonical one to one correspondence between all betweenness relations satisfying certain axioms and all pairs of inverse orderings defined on X for which the corresponding Hasse diagram is connected and all maximal chains contain at least 3 elements. By adding one more axiom, a one to one correspondence to lattices follows.

Keywords:

Ordered sets, lattices, betweenness relations, Hasse diagrams, graphs

Language:

English

Publication time:

5 / 2003