#15431: Transversal Design TD(6,12)
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | 4adf6b5792919daea356c66d511fc621776d0a77
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/15431 |
Dependencies: |
#15287 #15368 |
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Comment (by ncohen):
Hellooooo !
> I am very happy with the `EmptySetError`. Could you raise it *before*
the check t=2 ?
I believe it is already the case in the branch.
> OA and TD are the same objects up to relabeling.
Yep !
> More precisely, an OA is a TD with sets V1 = V2 = ... = Vn = [n] whereas
you choose the convention V1 = [n], V2 = [n,2n], ... for the TD. I do not
see the point of having two different functions... please tell me.
Well, I have two because I implemented all this while reading books and
fishing for the theorems I needed. It is true that they are the same, and
there is also a bijection between orthogonal arrays with `t=2` and
mutually orthogonal latin squares. That's why I would like to "implement
the theorem" that "There exists a TD iif there exists a OA iif there
exists a MOLS", and make sure that if one of the three functions can build
something then the two others can build the corresponding object.
Why a TD and a OA ? Well, because the books talk of both. Sometimes the
same book talks of the two things, and sometimes you do not want to do
this relabeling by yourself. They are the same objects (as well as MOLS)
and so the code must not repeat itself, but the two objects exist in the
book and so I think the two objects should exist here too.
As any construction of a MOLS or OA or TD can be translated into a
construction of another of the three, it is technically possible to have
only one main function, and two "translating" functions when needed. But
those constructions I found in books are already quite unclear, there is
already a lot of relabelling being done "silently" in the constructions,
and I thought it could only help to write the constructions in their
original formalism instead of translating them. Plus it would really be a
pain to translate all the proofs while reading them, what I wrote was not
thaaaaat easy to translate into code already `:-P`
> It seems that backtracking might be an approach to build TD when there
are no other constructions. It might also be helpful to build all TD up to
isomorphism. Do you know how hard would it be ?
I have got no idea on earth. This stuff scares me. For me eveything which
is related to designs is black magic.
> Curiosity question: if you build a TD with k=n+t-1 do we know if for any
two Si, Sj their intersection has t-1 elements ? (answering yes would help
the backtracking)
What are Si and Sj ?
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/15431#comment:11>
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