6 papers
Constructing/analyzing differential distributed lattices
Dale R. Worley
We restate a process presented by Stanley as a technique to prove that there exists exactly one -differential distributive lattice for any positive integer . This process can…
An extension of Birkhoff's representation theorem to locally-finite distributive lattices
Dale R. Worley
Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the part…
On the structure of modular lattices -- Axioms for gluing
Dale R. Worley
This paper explores alternative statements of the axioms for lattice gluing, focusing on lattices that are modular, locally finite, and have finite covers, but may have infinite he…
On the structure of modular lattices -- Unique gluing and dissection
Dale R. Worley
This work proves that the process of gluing finite lattices to form a larger lattice is bijective, that is each lattice is the glued sum of a unique system of finite lattices, prov…
S-Glued sums of lattices
Christian Herrmann, Dale R. Worley
For many equation-theoretical questions about modular lattices, Hall and Dilworth give a useful construction: Let be a lattice with largest element , be a lattice…
A survey of lattice properties: modular, Arguesian, linear, and distributive
Dale R. Worley
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some…