Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Collection of Finite Lattices Generated by a Poset
Journal: Order: A Journal on the Theory of Ordered Sets and its Applications
Volume: 17
Issue: 2
First page: 129
Last page: 139
Issue Date: 1-Jan-2000
Rank: M23
ISSN: 0167-8094
DOI: 10.1023/A:1006473619786
Abstract: 
It is proved that the collection of all finite lattices with the same partially ordered set of meet-irreducible elements can be ordered in a natural way so that the obtained poset is a lattice. Necessary and sufficient conditions under which this lattice is Boolean, distributive and modular are given.
Keywords: Finite distributive lattice | Finite lattice | Meet-irreducible | Representation of lattices
Publisher: Springer Link

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