Covers in free lattices

Author:

Freese Ralph,Nation J. B.

Abstract

In this paper we study the covering relation ( u v ) (u \succ v) in finitely generated free lattices. The basic result is an algorithm which, given an element w FL ( X ) w \in {\text {FL}}(X) , finds all the elements which cover or are covered by w w (if any such elements exist). Using this, it is shown that covering chains in free lattices have at most five elements; in fact, all but finitely many covering chains in each free lattice contain at most three elements. Similarly, all finite intervals in FL ( X ) {\text {FL}}(X) are classified; again, with finitely many exceptions, they are all one-, two- or three-element chains.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference19 articles.

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