CONGRUENCE LATTICES OF SMALL PLANAR LATTICES

Authors
GRATZER G LAKSER H SCHMIDT ET
Citation
G. Gratzer et al., CONGRUENCE LATTICES OF SMALL PLANAR LATTICES, Proceedings of the American Mathematical Society, 123(9), 1995, pp. 2619-2623
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
9
Year of publication
1995
Pages
2619 - 2623
Database
ISI
SICI code
0002-9939(1995)123:9<2619:CLOSPL>2.0.ZU;2-K
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 th at the congruence lattice of L is isomorphic to D. This improves on an early result of R. P. Dilworth (around 1940) and G. Gratzer and E. T. Schmidt (1962) constructing such a (nonplanar) lattice L with O(2(2n) ) elements, and on a recent construction of G. Gratzer and H. Lakser w hich yields a finite (planar) lattice L with O(n(3)) elements.