Lattices with many congruences are planar

2018/07/22 by Gábor Czédli, Czédli, Gábor
Computer Science · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1807.08384

Abstract

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

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