Lattices with many congruences are planar
Gábor Czédli · Algebra Universalis · 2019
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.