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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Congruence lattices of small planar lattices


Authors: G. Grätzer, H. Lakser and E. T. Schmidt
Journal: Proc. Amer. Math. Soc. 123 (1995), 2619-2623
MSC: Primary 06B10; Secondary 06D05
MathSciNet review: 1301498
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Abstract: For a finite distributive lattice D with n join-irreducible elements, we construct a finite (planar) lattice L with $ O({n^2})$ elements such that the congruence lattice of L is isomorphic to D. This improves on an early result of R. P. Dilworth (around 1940) and G. Grätzer and E. T. Schmidt (1962) constructing such a (nonplanar) lattice L with $ O({2^{2n}})$ elements, and on a recent construction of G. Grätzer and H. Lakser which yields a finite (planar) lattice L with $ O({n^3})$ elements.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1301498-5
PII: S 0002-9939(1995)1301498-5
Keywords: Lattice, finite, congruence, distributive, planar
Article copyright: © Copyright 1995 American Mathematical Society