#20980: LatticePoset: certificate for non-modularity, part 1
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues: rebase over 7.3.beta7
Branch: | Commit:
public/test_branch_find_pentagon | 6043924acb37777cf7daa5f8a143d31d85bfd817
Dependencies: | Stopgaps:
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Comment (by kdilks):
Ok, I've spent a bit of time convincing myself the math works out with the
description, and I think it needs some clarification.
Strictly speaking, what the description mentions corresponds to Birkhoff's
condition for weak semimodularity. Just looking at the definition of
semimodularity, it appears one only needs a pair of elements `a` and `b`
so that `a` covers the meet and `b` is not covered by the join. It's only
because weakly semimodular is equivalent to semimodular for finite
lattices* that we can further require that `b` covers the meet and `a` is
covered by the join.
*(technically lattices of finite length and upper continuous relatively
atomic lattices...whatever that means)
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Ticket URL: <https://trac.sagemath.org/ticket/20980#comment:10>
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