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

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