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Results tagged with combinatorial-designs
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user 2233
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.
6
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Accepted
Minimum covers of complete graphs by $4$-cycles
If $n$ is odd, the answer is $\lceil \binom{n}{2}/4 \rceil$.
If $n$ is even, the answer is $\lceil \binom{n}{2}/4+n/8 \rceil$.
This follows from two special cases of a more general conjecture by Als …
- 32.1k
6
votes
Intersecting 4-sets
For all even $n \geq 16$, $N:=\binom{n/2}{2}$ is the right answer.
Semi-proof. Let $n=2k$ and observe that $4N=2k(k-1)$. Thus, if more than $N$ sets appear, then some element $x$ occurs in at leas …
- 32.1k