#19197: LatticePoset: add breadth()
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/latticeposet__add_breadth__|
8d81130c3ea697cbfe3ce178dd5a7fac052e78d3
Dependencies: | Stopgaps:
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Comment (by jmantysalo):
Replying to [comment:2 ncohen]:
> Also, could you be a bit more formal in the definition of 'breadth'? I
did not follow it at first (english is not a well-paenthesized language).
It would also be cool if you could redirect toward a textbook/paper that
defines it: I found it in "Semimodular Lattices Theory and Applications"
where it is said to originate from "Lattice Theory" by Birkhoff.
True. "- - of the ''breadth'' of a lattice ''L'', - - as the least
positive integer ''b = b[L]'' such that any meet ''x_1 `^` . . . `^` x_n
[n > b]'' is always a meet of a subset of ''b'' of the ''x_i''. This is on
p. 99. Not very intuitive definition... So let's try from scratch:
Let `E` be an `n`-element subset of elements of the lattice, `j` be a join
of `E`, and join of every proper subset of `E` be not equal `j`. The
''breadth'' of lattice is number of elements in a largest such subset `E`.
? Hmm... not best possible.
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Ticket URL: <http://trac.sagemath.org/ticket/19197#comment:8>
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