#16866: Radical difference families
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.4
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | 721af75ec2b2c6ca904f2feaf86e75e054cb089d
u/vdelecroix/16866 | Stopgaps:
Dependencies: #16863 |
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Comment (by vdelecroix):
Replying to [comment:16 ncohen]:
> Yo !
>
> > `A` appears explicitly when you compute `\Delta
{1,r,r^2,...,r^(k-1)\}`. Its definition is obtained from differences
already.
>
> I still don't get it. I expect to have a set of cardinality `k(k-1)` and
I don't find it anywhere.
True but there is a formula in my docstring:
{{{
It is easy to verify (see [Wi72]_) that we have for `k` odd `\Delta
H^{2mt}
= A H^{mt}` while for `k` even `\Delta (H^{2mt} \cup \{0\}) = A
H^{mt}`.
Here `\Delta B` is the set of differences of distinct elements in `B`.
}}}
And you can check that `# (A H^{mt}) = #A # H^{mt}` has cardinality
k(k-1).
> > True. But I wonder if we can do better for that particular problem. I
also thought about moving it in some tiling stuff in `sage.combinat`. That
way it would be better advertised.
>
> Well, if it belongs to some tiling library (but really, for me tiling
and packing are the same things..) and has a more meaningful name then no
problem of course.
Right, tiling/packing I do not care but there exists
`sage.combinat.tiling` for some 2-dimensional tilings with polyominos.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16866#comment:17>
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