Congruence lattices of small planar lattices
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- by G. Grätzer, H. Lakser and E. T. Schmidt PDF
- Proc. Amer. Math. Soc. 123 (1995), 2619-2623 Request permission
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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2619-2623
- MSC: Primary 06B10; Secondary 06D05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301498-5
- MathSciNet review: 1301498