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Planar Sublattices of a Free Lattice. II

Published online by Cambridge University Press:  20 November 2018

Ivan Rival  and
Bill Sands
Ivan Rival
Affiliation:
University of Calgary, Calgary, Alberta
Bill Sands
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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In Planar sublattices of a free lattice, I [8] we verify Jonsson's conjecture for finite planar lattices; in particular we obtain a characterization of finite planar sublattices of a free lattice among all finite lattices. In the present paper we use arguments of a quite different flavour to obtain another characterization. Let

be the family of lattices illustrated in Figures 1, 2, 3, and 4. Our goal is to prove the following theorem: a finite lattice is a planar sublattice of a free lattice if andonly if it does not have a member of as a sublattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 17 - 34
Copyright
Copyright © Canadian Mathematical Society 1979

References

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