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1997•Proceedings of the American Mathematical SocietyOpen access

Computing congruence lattices of finite lattices

Ralph Freese

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Abstract

An inequality between the number of coverings in the ordered set J ⁡ ( C o n J ) \operatorname {J}({\mathbf {Con\;J}}) of join irreducible congruences on a lattice L \operatorname {L} and the size of L {\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 ) O(n^2 \log _2 n) , where n = | L | n=|L| .

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An inequality between the number of coverings in the ordered set J ⁡ ( C o n J ) \operatorname {J}({\mathbf {Con\;J}}) of join irreducible congruences on a lattice L \operatorname {L} and the size of L {\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 ) O(n^2 \log _2 n) , where n = | L | n=|L| .

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Available abstract

An inequality between the number of coverings in the ordered set J ⁡ ( C o n J ) \operatorname {J}({\mathbf {Con\;J}}) of join irreducible congruences on a lattice L \operatorname {L} and the size of L {\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 ) O(n^2 \log _2 n) , where n = | L | n=|L| .

Key concepts: Congruence (geometry), Congruence relation, Mathematics, Join (topology), Lattice (music), Combinatorics, Inequality, Complete lattice

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