Gábor Czédli
Abstract
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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.
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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.
Key concepts: Congruence relation, Planar, Mathematics, Lattice (music), Complete lattice, Natural number, Combinatorics, Pure mathematics