2017/08/31 by Henri Mühle · 10 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Core (optical fiber) #Distributive lattice #Fuzzy and Soft Set Theory #Hyperplane #Lattice (music) #Map of lattices #Order (exchange) #Partially ordered set #Property (philosophy) #Rough Sets and Fuzzy Logic #math.CO #msc:06A07 #msc:06B05
paper · pdf · doi:10.1007/s00012-019-0585-5
published in Algebra Universalis 80(1) (Birkhäuser) · 19 pages, 9 figures, 1 table. Final version. Comments are welcome
openalex created_date 2018/11/29 · arxiv created 2019/01/14 · openalex publication_date 2019/02/05 · arxiv updated 2019/04/12 · openalex updated_date 2026/08/05
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.