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Results tagged with combinatorial-designs
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user 11100
Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
4
votes
Constructing Group Divisible Designs - Algorithms?
There are some implementations available in sagemath, see e.g. http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/designs/group_divisible_designs.html#sage-combinat-designs-group-divisib …
- 14k
4
votes
Self-complementary block designs
There is an example for $n=6$, a quite exceptional one. It comes from the smallest finite sporadic simple group $G=M_{11}$ of order 7920. $G$ has a permutation representation on 12 points, correspondi …
- 14k
7
votes
Accepted
Combinatorial designs textbook recommendation
There is a list of references in
http://www.maths.qmul.ac.uk/~pjc/design/resources.html#books
and
http://en.wikipedia.org/wiki/Block_design#References
From the latter, I know books by Beth et al (a …
- 14k
5
votes
Intersecting 4-sets
It looks like the conjecture is very close to be right (i.e. $N$ is an upper bound) for $n\geq 12$, as the linear programming (LP) bound equals $N$ for even $n$ even, $500\geq n\geq 12$.
When $n$ is o …
- 14k
5
votes
Minimally intersecting subsets of fixed size
This is a coding theory question. You want to find a binary constant weight $m$ code with $k$ codewords, and of maximal possible distance.
There was a lot of research done on this.
For the specific c …
- 14k