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On Dualization over Distributive Lattices
[article]

2022
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arXiv
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pre-print

Given a partially order set (poset) P, and a pair of families of ideals ℐ and filters ℱ in P such that each pair (I,F)∈ℐ×ℱ has a non-empty intersection, the dualization problem over P is to check whether there is an ideal X in P which intersects every member of ℱ and does not contain any member of ℐ. Equivalently, the problem is to check for a distributive lattice L=L(P), given by the poset P of its set of joint-irreducibles, and two given antichains 𝒜,ℬ⊆ L such that no a∈𝒜 is dominated by any

arXiv:2006.15337v4
fatcat:2eqgc3ldmnfbdkzbjoy2pv7dxu