#16534: Basic Block design methods
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Reporter: brett | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: Block Design, | Reviewers:
Incidence Structure, Residual, | Work issues:
Derived, Complement, Supplement, | Commit:
Union | 13280d995c98d13fbf2b9637411d3988999453e1
Authors: Brett Stevens | Stopgaps:
Report Upstream: N/A |
Branch: u/brett/design |
Dependencies: #16553 |
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Comment (by brett):
Replying to [comment:33 ncohen]:
> > An incidence structure is group divisible iff its dual is resolvable
so the is_resolvable method can be used to determine if the IS is group
divisible. The question is if we find that a IS is group divisible, what
do we want to do. Do we want to store the groups as a part fo the IS?
>
> From your question I wonder if we are talking about the same thing. I
was simply saying that we have a function `is_group_divisible_design` that
tells you if an incidence structure is a group divisible design. Is that
also what you have in mind?
It looks to me as if your is_group_divisible_design requires the use to
hand the method the groups.
I was thinking of building a function to determine if a deign is group
divisible without knowing what the groups might be.
I was slightly incorrect before. A more accurate statement would be that
the dual of a resolvable IS is an group divisible IS with the property
that the blocks are transversal.
It is important to note that neither may be designs.
This fact follows from dualising thew definition of resolvable:
A IS is resolvable if there exists a partition of the blocks into classes
such that every point is incident with exactly one block in each class.
the dual of this statement is
there exists a partition of the points into classes (groups) such that
every block is incident with exactly one point in each class (group)
>
> In particular, I do not understand how that could be equivalent to
finding out whether the dual is resolvable: we have a `.is_resolvable`
function, but it is rather slow.
--
Ticket URL: <http://trac.sagemath.org/ticket/16534#comment:35>
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