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Representation of lattices via set-colored posets
- Source :
- Discrete Applied Mathematics, Discrete Applied Mathematics, Elsevier, 2018, 249, pp.64-73. ⟨10.1016/j.dam.2018.03.068⟩, Discrete Applied Mathematics, 2018, 249, pp.64-73. ⟨10.1016/j.dam.2018.03.068⟩
- Publication Year :
- 2018
- Publisher :
- HAL CCSD, 2018.
-
Abstract
- International audience; This paper proposes a representation theory for any finite lattice via set-colored posets, in the spirit of Birkhoff for distributive lattices. The notion of colored posets was introduced in Nourine (2000) [34] and the generalization to set-colored posets was given in Nourine (2000) [35]. In this paper, we give a characterization of set-colored posets for general lattices, and show that set-colored posets capture the order induced by join-irreducible elements of a lattice as Birkhoff’s representation does for distributive lattices. We also give a classification for some lattices according to the coloring property of their set-colored representation including upper locally distributive, upper locally distributive, meet-extremal and semidistributive lattices.
- Subjects :
- Antimatroid
Set-colored poset
Applied Mathematics
High Energy Physics::Lattice
010102 general mathematics
Lattice
Representation theory
Upper locally distributive lattice
0102 computer and information sciences
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
16. Peace & justice
01 natural sciences
Combinatorics
Closure system
Colored
Distributive property
010201 computation theory & mathematics
Lattice (order)
Discrete Mathematics and Combinatorics
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Database :
- OpenAIRE
- Journal :
- Discrete Applied Mathematics, Discrete Applied Mathematics, Elsevier, 2018, 249, pp.64-73. ⟨10.1016/j.dam.2018.03.068⟩, Discrete Applied Mathematics, 2018, 249, pp.64-73. ⟨10.1016/j.dam.2018.03.068⟩
- Accession number :
- edsair.doi.dedup.....7ebbf7513e28dce77179d6c94102cee9