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Results tagged with combinatorial-designs
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user 3402
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.
1
vote
Minimum covers of complete graphs by $4$-cycles
If n is even, you can form a partial edge cover with disjoint four-cycles: pick points u and v, and cover all edges coming from u and from v (except for uv) by disjoint cycles. Now recurse, leaving n/ …
- 13k
6
votes
Status of Hadamard matrix conjecture
With all due respect to Colin McLarty, here is (in my not so humble opinion) a better answer.
The conjecture (For every positive integer $k,$ there is a square matrix $H$ of order $4k$ such that $H$ …
- 13k
3
votes
Maximum determinant of $\{0,1\}$-valued $n\times n$-matrices
( I assume the R in the title is the real numbers. For arbitrary rings R an order needs
to be specified before remarks like those below should be made. )
Using the method suggested by Robin Chapman, …
- 13k