Like that
sage: p = posets.DiamondPoset(6)
sage: h = p.hasse_diagram()
sage: [h.all_paths(x,y) for x in h for y in p.principal_order_filter(x)]
[[[0]],
[[0, 1]],
[[0, 2]],
[[0, 3]],
[[0, 4]],
[[0, 1, 5], [0, 2, 5], [0, 3, 5], [0, 4, 5]],
[[1]],
[[1, 5]],
[[2]],
[[2, 5]],
[[3]],
[[3, 5]],
[[4]],
[[4, 5]],
[[5]]]
Asked: 2018-09-01 02:16:47 +0100
Seen: 747 times
Last updated: Sep 03 '18
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This is not my field so I can ask a silly question: Is every saturated chain a subchain of a maximal chain?
See also Stack Overflow question 52105780.
Yes. Every saturated chain is a maximal chain of a subposet.
My naive idea was to take all subchains of all maximal chains. This works, but it is inefficient because you get duplicates.