The core label order of a congruence-uniform lattice
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
We investigate the alternate order on a congruence-uniform lattice L as introduced by N. Reading, which we dub the core label order of L. When L can be realized as a poset of regions of a simplicial hyperplane arrangement, the core label order is always a lattice. For general L, however, this fails. We provide an equivalent characterization for the core label order to be a lattice. As a consequence we show that the property of the core label order being a lattice is inherited to lattice quotients. We use the core label order to characterize the congruence-uniform lattices that are Boolean lattices, and we investigate the connection between congruence-uniform lattices whose core label orders are lattices and congruence-uniform lattices of biclosed sets.
Details
Originalsprache | Englisch |
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Aufsatznummer | 10 |
Fachzeitschrift | Algebra universalis |
Jahrgang | 80 |
Ausgabenummer | 1 |
Publikationsstatus | Veröffentlicht - 1 März 2019 |
Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Biclosed sets, Congruence-uniform lattices, Crosscut theorem, Interval doubling, Möbius function, Semidistributive lattices