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Algebra universalis

, 80:16 | Cite as

Lattices with many congruences are planar

  • Gábor CzédliEmail author
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Abstract

Let L be an n-element finite lattice. We prove that if L has more than \(2^{n-5}\) congruences, then L is planar. This result is sharp, since for each natural number \(n\ge 8\), there exists a non-planar lattice with exactly \(2^{n-5}\) congruences.

Keywords

Planar lattice Lattice congruence Congruence lattice 

Mathematics Subject Classification

06B10 

Notes

Acknowledgements

The referee’s historical comment calling the author’s attention to Crawley and Dilworth [2] and to Dilworth [4] is highly appreciated.

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Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary

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