Computing congruence lattices of finite lattices

Freese, Ralph

doi:10.1090/S0002-9939-97-04332-3

Computing congruence lattices of finite lattices
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Proc. Amer. Math. Soc. 125 (1997), 3457-3463 Request permission

Abstract:

An inequality between the number of coverings in the ordered set $\operatorname {J}({\mathbf {Con\;J}})$ of join irreducible congruences on a lattice $\operatorname {L}$ and the size of ${\mathbf {L}}$ is given. Using this inequality it is shown that this ordered set can be computed in time $O(n^2 \log _2 n)$, where $n=|L|$.

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