Distributive lattices have the intersection property
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite distributive lattice is always a meet-semilattice.
Details
Originalsprache | Englisch |
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Seiten (von - bis) | 7-17 |
Seitenumfang | 11 |
Fachzeitschrift | Mathematica Bohemica |
Jahrgang | 146 |
Ausgabenummer | 1 |
Publikationsstatus | Veröffentlicht - 2021 |
Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Canonical join complex, Congruence-uniform lattice, Core label order, Distributive lattice, Intersection property