A note on finite lattices with many congruences

Abstract

By a twenty year old result of Ralph Freese, an $n$-element lattice $L$ has at most $2^{n-1}$ congruences. We prove that if $L$ has less than $2^{n-1}$ congruences, then it has at most $2^{n-2}$ congruences. Also, we describe the $n$-element lattices with exactly $2^{n-2}$ congruences.

5 pages, 2 figures

Cited by in corpus (1)

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