Display concept lattices

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0. All ortholattices with up to 6 join-irreducible elements:
[
// 2 join-irreducibles
[[1], [0]],
// 3 join-irreducibles
[[1, 2], [0, 2], [0, 1]],
// 4 join-irreducibles
[[1], [0], [3], [2]],
[[1, 2], [0], [0, 3], [2]],
[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]],
// 5 join-irreducibles
[[1, 4], [0, 2], [1, 3], [2], [0]],
[[1, 4], [0, 2], [1, 3], [2, 4], [0, 3]],
[[1, 2, 4], [0, 2], [0, 1, 3], [2, 4], [0, 3]],
[[1, 2, 3, 4], [0, 2], [0, 1, 3], [0, 2, 4], [0, 3]],
[[1, 2, 3, 4], [0, 2, 3, 4], [0, 1, 3, 4], [0, 1, 2, 4], [0, 1, 2, 3]],
[[1, 4], [0, 4], [3], [2], [0, 1]],
[[1, 2, 4], [0, 4], [0, 3], [2], [0, 1]],
[[1, 2, 4], [0, 2, 4], [0, 1, 3], [2], [0, 1]],
[[1, 2, 3, 4], [0, 4], [0, 3], [0, 2], [0, 1]],
// 6 join-irreducibles
[[1, 3, 4], [0, 4], [3, 5], [0, 2], [0, 1], [2]],
[[1, 3, 4], [0, 2, 4], [1, 3, 5], [0, 2], [0, 1], [2]],
[[1, 4], [0, 4], [3, 5], [2, 5], [0, 1], [2, 3]], 
[[1, 2, 4], [0, 4], [0, 3, 5], [2, 5], [0, 1], [2, 3]],
[[1, 2, 4], [0, 2, 4], [0, 1, 3, 5], [2, 5], [0, 1], [2, 3]], 
[[1, 2, 4], [0, 2, 4], [0, 1, 3, 4, 5], [2, 5], [0, 1, 2], [2, 3]], 
[[1], [0], [3], [2], [5], [4]], 
[[1, 2], [0], [0, 3], [2], [5], [4]], 
[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2], [5], [4]], 
[[1, 2, 4], [0, 2, 3], [0, 1, 3], [1, 2], [0, 5], [4]], 
[[1, 2, 3, 4], [0, 2, 3], [0, 1, 3], [0, 1, 2], [0, 5], [4]], 
[[1, 2, 4], [0, 2, 3, 4], [0, 1, 3], [1, 2], [0, 1, 5], [4]], 
[[1, 2, 3, 4], [0, 2, 3], [0, 1, 3], [0, 1, 2, 4], [0, 3, 5], [4]], 
[[1, 2, 3, 4], [0, 2, 3, 4], [0, 1, 3], [0, 1, 2, 4], [0, 1, 3, 5], [4]], 
[[1, 2], [0, 4], [0, 3], [2], [1, 5], [4]], 
[[1, 2, 4], [0, 2, 4], [0, 1, 3], [2], [0, 1, 5], [4]], 
[[1, 2], [0, 4], [0, 3, 4], [2], [1, 2, 5], [4]], 
[[1, 2], [0, 4], [0, 3], [2, 5], [1, 5], [3, 4]], 
[[1, 2], [0, 2, 4], [0, 1, 3], [2, 5], [1, 5], [3, 4]], 
[[1, 2, 3], [0, 2, 4], [0, 1, 3], [0, 2, 5], [1, 5], [3, 4]], 
[[1, 2, 3], [0, 2, 3, 4], [0, 1, 3], [0, 1, 2, 5], [1, 5], [3, 4]], 
[[1, 2, 3, 4], [0, 2, 4], [0, 1, 3], [0, 2, 5], [0, 1, 5], [3, 4]],
[[1, 2, 3, 4], [0, 2, 3, 4], [0, 1, 3], [0, 1, 2, 5], [0, 1, 5], [3, 4]],
[[1, 2, 3, 4], [0, 2, 3, 4], [0, 1, 3], [0, 1, 2, 4, 5], [0, 1, 3, 5], [3, 4]], 
[[1, 2, 3, 4], [0, 2, 4], [0, 1, 3], [0, 2, 4, 5], [0, 1, 3, 5], [3, 4]], 
[[1, 2, 3, 4, 5], [0, 2, 4], [0, 1, 3], [0, 2, 5], [0, 1, 5], [0, 3, 4]], 
[[1, 2, 3], [0, 2, 4], [0, 1, 3], [0, 2, 4, 5], [1, 3, 5], [3, 4]], 
[[1, 2, 3], [0, 2, 3, 4], [0, 1, 3], [0, 1, 2, 4, 5], [1, 3, 5], [3, 4]], 
[[1, 2, 3], [0, 2, 3, 4, 5], [0, 1, 3], [0, 1, 2, 4, 5], [1, 3, 5], [1, 3, 4]], 
[[1, 2], [0, 2, 4], [0, 1, 3], [2, 4, 5], [1, 3, 5], [3, 4]], 
[[1, 2], [0, 2, 3, 4], [0, 1, 3], [1, 2, 4, 5], [1, 3, 5], [3, 4]], 
[[1, 2], [0, 2, 4, 5], [0, 1, 3], [2, 5], [1, 5], [1, 3, 4]], 
[[1, 2], [0, 2, 4, 5], [0, 1, 3, 5], [2, 5], [1, 5], [1, 2, 3, 4]], 
[[1, 2], [0, 3, 4], [0, 3], [1, 2, 5], [1, 5], [3, 4]], 
[[1, 2], [0, 2, 3, 4], [0, 1, 3], [1, 2, 5], [1, 5], [3, 4]], 
[[1, 2], [0, 2, 3, 4, 5], [0, 1, 3], [1, 2, 5], [1, 5], [1, 3, 4]],
[[1, 2, 4], [0, 3, 4], [0, 3], [1, 2, 5], [0, 1, 5], [3, 4]], 
[[1, 2, 4], [0, 3, 4], [0, 3, 5], [1, 2, 5], [0, 1, 5], [2, 3, 4]], 
[[1, 2, 4], [0, 2, 3, 4], [0, 1, 3, 5], [1, 2, 5], [0, 1, 5], [2, 3, 4]], 
[[1, 2, 4], [0, 2, 3, 4], [0, 1, 3, 4, 5], [1, 2, 5], [0, 1, 2, 5], [2, 3, 4]],
[[1, 2, 4], [0, 2, 3, 4], [0, 1, 3, 4, 5], [1, 2, 4, 5], [0, 1, 2, 3, 5], [2, 3, 4]],
[[1, 2, 3, 4, 5], [0, 2, 3, 4, 5], [0, 1, 3, 4, 5], [0, 1, 2, 4, 5], [0, 1, 2, 3, 5], [0, 1, 2, 3, 4]],
[[1, 2], [0, 2, 3, 4], [0, 1, 3, 4], [1, 2, 4, 5], [1, 2, 3, 5], [3, 4]]]

1. All 7 reduced separated 3x3 contexts (i.e. all finite lattices with 3 join-irreducible and 3 meet-irreducible elements) 
[
[[], [0], [0, 1], [0, 1, 2]], 
[[], [0, 1], [0, 2]], 
[[0], [1], [2]], 
[[0], [1], [0, 1], [0, 1, 2]], 
[[0], [1], [0, 2]], 
[[0], [0, 1], [1, 2]], 
[[0, 1], [0, 2], [1, 2]]
]
2. All reduced separated 3x4 contexts 
[
[[0], [1, 2], [1, 3]],
[[0, 1], [0, 2], [1, 3]]
]
3. All 45 reduced separated 4x4 contexts 
[
[[], [0], [0, 1], [0, 1, 2]],
[[], [0], [0, 1, 2], [0, 1, 3]],
[[], [0, 1], [0, 2], [0, 3]],
[[], [0, 1], [0, 2], [0, 1, 2]],
[[], [0, 1], [0, 2], [0, 1, 3]],
[[], [0, 1], [0, 1, 2], [0, 2, 3]],
[[], [0, 1, 2], [0, 1, 3], [0, 2, 3]],
[[0], [1], [2], [3]],
[[0], [1], [2], [0, 3]],
[[0], [1], [2], [0, 1, 2]],
[[0], [1], [0, 1], [0, 1, 2]],
[[0], [1], [0, 2], [1, 3]],
[[0], [1], [0, 2], [2, 3]],
[[0], [1], [0, 2], [0, 1, 2]],
[[0], [1], [0, 2], [0, 2, 3]],
[[0], [1], [2, 3], [0, 1, 2]],
[[0], [1], [0, 1, 2], [0, 1, 3]],
[[0], [1], [0, 1, 2], [0, 2, 3]],
[[0], [0, 1], [2, 3], [0, 1, 2]],
[[0], [0, 1], [0, 1, 2], [1, 2, 3]],
[[0], [1, 2], [0, 1], [1, 3]],
[[0], [1, 2], [0, 1], [2, 3]],
[[0], [1, 2], [0, 1], [0, 1, 2]],
[[0], [1, 2], [0, 1], [0, 1, 3]],
[[0], [1, 2], [0, 1], [1, 2, 3]],
[[0], [1, 2], [1, 3], [2, 3]],
[[0], [1, 2], [1, 3], [0, 1, 2]],
[[0], [1, 2], [1, 3], [0, 2, 3]],
[[0], [1, 2], [1, 3], [1, 2, 3]],
[[0], [1, 2], [0, 1, 2], [0, 1, 3]],
[[0], [1, 2], [0, 1, 3], [0, 2, 3]],
[[0], [1, 2], [1, 2, 3], [0, 1, 3]],
[[0], [0, 1, 2], [0, 1, 3], [1, 2, 3]],
[[0, 1], [0, 2], [1, 2], [0, 1, 2]],
[[0, 1], [0, 2], [1, 2], [0, 1, 3]],
[[0, 1], [0, 2], [0, 3], [1, 2]],
[[0, 1], [0, 2], [0, 3], [1, 2, 3]],
[[0, 1], [0, 2], [0, 1, 2], [1, 2, 3]],
[[0, 1], [0, 2], [0, 1, 3], [1, 2, 3]],
[[0, 1], [2, 3], [0, 2], [1, 3]],
[[0, 1], [2, 3], [0, 2], [0, 1, 2]],
[[0, 1], [2, 3], [0, 2], [0, 1, 3]],
[[0, 1], [2, 3], [0, 1, 2], [0, 2, 3]],
[[0, 1], [0, 2, 3], [0, 1, 2], [1, 2, 3]],
[[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]]
]
4. All 50 reduced separated 4x5 contexts 
[
[[], [0, 1], [0, 2, 3], [0, 2, 4]],
[[], [0, 1, 2], [0, 1, 3], [0, 2, 4]],
[[0], [1], [2, 3], [2, 4]],
[[0], [1], [0, 2, 3], [0, 2, 4]],
[[0], [0, 1], [1, 2, 3], [1, 2, 4]],
[[0], [1, 2], [1, 3], [0, 4]],
[[0], [1, 2], [1, 3], [1, 4]],
[[0], [1, 2], [1, 3], [2, 4]],
[[0], [1, 2], [1, 3], [1, 2, 4]],
[[0], [1, 2], [1, 3], [0, 1, 2, 3]],
[[0], [1, 2], [3, 4], [0, 1, 3]],
[[0], [1, 2], [0, 1, 3], [0, 1, 4]],
[[0], [1, 2], [0, 1, 3], [0, 3, 4]],
[[0], [1, 2], [0, 1, 3], [1, 3, 4]],
[[0], [1, 2], [1, 2, 3], [1, 3, 4]],
[[0], [1, 2], [1, 3, 4], [0, 1, 2, 3]],
[[0], [1, 2, 3], [0, 1, 2], [0, 1, 4]],
[[0], [1, 2, 3], [0, 1, 2], [1, 3, 4]],
[[0], [1, 2, 3], [1, 2, 4], [1, 3, 4]],
[[0], [1, 2, 3], [1, 2, 4], [0, 1, 3, 4]],
[[0, 1], [0, 2], [0, 3], [1, 4]],
[[0, 1], [0, 2], [1, 3], [2, 4]],
[[0, 1], [0, 2], [1, 3], [0, 1, 4]],
[[0, 1], [0, 2], [1, 3], [0, 2, 4]],
[[0, 1], [0, 2], [1, 3], [0, 1, 2, 3]],
[[0, 1], [0, 2], [3, 4], [0, 1, 3]],
[[0, 1], [0, 2], [3, 4], [1, 2, 3]],
[[0, 1], [0, 2], [3, 4], [0, 1, 2, 3]],
[[0, 1], [0, 2], [0, 1, 3], [1, 3, 4]],
[[0, 1], [0, 2], [1, 2, 3], [1, 2, 4]],
[[0, 1], [0, 2], [1, 2, 3], [1, 3, 4]],
[[0, 1], [0, 2], [1, 3, 4], [0, 1, 2, 3]],
[[0, 1], [2, 3], [0, 1, 2], [0, 2, 4]],
[[0, 1], [2, 3], [0, 2, 4], [0, 1, 4]],
[[0, 1], [2, 3], [0, 2, 4], [1, 2, 4]],
[[0, 1], [2, 3], [0, 2, 4], [1, 3, 4]],
[[0, 1], [2, 3], [0, 2, 4], [0, 1, 2, 3]],
[[0, 1], [2, 3], [0, 2, 4], [0, 1, 3, 4]],
[[0, 1], [0, 2, 3], [0, 1, 2], [1, 2, 4]],
[[0, 1], [0, 2, 3], [0, 1, 2], [2, 3, 4]],
[[0, 1], [0, 2, 3], [1, 2, 3], [0, 2, 4]],
[[0, 1], [0, 2, 3], [0, 2, 4], [1, 3, 4]],
[[0, 1], [0, 2, 3], [0, 2, 4], [2, 3, 4]],
[[0, 1], [0, 2, 3], [0, 2, 4], [1, 2, 3, 4]],
[[0, 1], [0, 2, 3], [1, 2, 4], [2, 3, 4]],
[[0, 1], [0, 2, 3], [1, 2, 4], [0, 1, 3, 4]],
[[0, 1], [0, 2, 3], [2, 3, 4], [0, 1, 2, 4]],
[[0, 1, 2], [0, 3, 4], [0, 1, 3], [1, 2, 3, 4]],
[[0, 1, 2], [0, 3, 4], [1, 2, 3], [0, 1, 3]],
[[0, 1, 2], [0, 3, 4], [1, 2, 3], [0, 1, 4]]
]
5. All 25 reduced separated 4x6 contexts 
[
[[0], [1, 2], [1, 3, 4], [1, 3, 5]],
[[0], [1, 2, 3], [1, 2, 4], [1, 3, 5]],
[[0], [1, 2, 3], [1, 4, 5], [0, 1, 2, 4]],
[[0, 1], [0, 2], [3, 4], [3, 5]],
[[0, 1], [0, 2], [1, 3, 4], [1, 3, 5]],
[[0, 1], [2, 3], [4, 5], [0, 2, 4]],
[[0, 1], [2, 3], [0, 2, 4], [0, 2, 5]],
[[0, 1], [2, 3], [0, 2, 4], [0, 4, 5]],
[[0, 1], [2, 3], [0, 4, 5], [0, 1, 2, 4]],
[[0, 1], [0, 2, 3], [2, 3, 4], [0, 2, 5]],
[[0, 1], [0, 2, 3], [2, 3, 4], [2, 4, 5]],
[[0, 1], [0, 2, 3], [1, 4, 5], [0, 1, 2, 4]],
[[0, 1], [0, 2, 3], [2, 4, 5], [0, 1, 2, 4]],
[[0, 1], [0, 2, 3], [2, 4, 5], [1, 2, 3, 4]],
[[0, 1], [2, 3, 4], [2, 3, 5], [0, 2, 4, 5]],
[[0, 1], [2, 3, 4], [0, 2, 3, 5], [1, 2, 4, 5]],
[[0, 1, 2], [0, 1, 3], [0, 2, 4], [1, 3, 5]],
[[0, 1, 2], [0, 3, 4], [1, 3, 5], [0, 1, 3]],
[[0, 1, 2], [0, 3, 4], [1, 3, 5], [2, 4, 5]],
[[0, 1, 2], [0, 3, 4], [1, 3, 5], [1, 2, 3, 4]],
[[0, 1, 2], [0, 3, 4], [1, 3, 5], [0, 2, 4, 5]],
[[0, 1, 2], [0, 3, 4], [0, 1, 3, 5], [1, 2, 4, 5]],
[[0, 1, 2], [3, 4, 5], [0, 1, 3], [0, 2, 3, 4]],
[[0, 1, 2], [3, 4, 5], [0, 1, 3, 4], [0, 2, 3, 5]],
[[0, 1, 2], [0, 1, 3, 4], [0, 2, 3, 5], [1, 2, 4, 5]]
]
6. All 4 reduced separated 4x7 contexts 
[
[[0, 1], [2, 3, 4], [2, 5, 6], [0, 2, 3, 5]],
[[0, 1, 2], [3, 4, 5], [0, 3, 6], [0, 1, 3, 4]],
[[0, 1, 2], [0, 3, 4, 5], [1, 3, 4, 6], [2, 3, 5, 6]],
[[0, 1, 2, 3], [0, 4, 5, 6], [1, 2, 4, 5], [1, 3, 4, 6]]
]

Peter Jipsen --- February 2020 --- Chapman University