#19197: LatticePoset: add breadth()
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers: Nathann Cohen
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/latticeposet__add_breadth__|
9c05f49e95504acc1a37ea942764886c53f57198
Dependencies: | Stopgaps:
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Comment (by jmantysalo):
Replying to [comment:30 ncohen]:
> By the way: it seems to me that, theoretically speaking, having breadth
`>=b` is equivalent to:
>
> {{{
> sage: G1 = my_lattice.hasse_diagram().transitive_closure()
> sage: G2 = posets.BooleanLattice(p).hasse_diagram().transitive_closure()
> sage: G1.subgraph_search(G2,induced=True)
> True
> }}}
And that is same as `L.has_isomorphic_subposet(Posets.BooleanLattice(b))`.
I guess you are right. (But not sure - must think about this.)
I made an example of smallest lattice with breadth 4 with
`completion_by_cuts()` and did not notice that the result was just
`BooleanLattice(4)`. Oops.
And that means that my example of lattice with breadth 4 is stupid, as it
hides the structure to dig6 string.
--
Ticket URL: <http://trac.sagemath.org/ticket/19197#comment:31>
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