Dual digraphs of finite meet-distributive and modular lattices
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Súbory
Dátum
2024
Názov časopisu
ISSN časopisu
Názov zväzku
Vydavateľ
Department of mathematics and statistics of the Universidad de La Frontera : Temuco
ISBN
ISSN
0716-7776
0719-0646
0719-0646
Abstrakt
We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digraphs. Combined with previous work in this journal on dual digraphs of semidistributive lattices (2022), it leads to a dual representation of finite meet-distributive lattices. This provides a natural link to finite convex geometries. In addition, we present two sufficient conditions on a finite TiRS digraph for its dual lattice to be modular. We close by posing three open problems.
Popis
In: Cubo : a mathematical journal. Temuco : Department of mathematics and statistics of the Universidad de La Frontera, 2024. ISSN 0716-7776. Vol. 26, no. 2 (2024), pp. 279-302.
Kľúčové slová
matematika, mathematics, algebra, teória zväzov, geometria, geometry
Výstup z projektu
VEGA 1/0152/22 Usporiadané algebraické štruktúry
Citácia
Práva a licenčné podmienky
CC BY-NC Creative Commons Attribution-NonCommercial 4.0. International
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess