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Results tagged with combinatorial-designs
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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.
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Is there a tournament schedule for 18 players, 17 rounds in groups of 6, which is balanced i...
A collection of $6$-tuples on 18 points with the property that each pair is covered $5$ times is a balanced incomplete block design with $(v,k,\lambda) = (18,6,5)$ and $t=2$. The condition that you ca …
- 28k
5
votes
How many elements with a hamming distance of 3 or less?
Here is a construction of size $38$. Call the points cards and divide the deck into $4$ suits, so that $2$ suits have ranks $1,...,13$ and $2$ suits have ranks $1,...,12$. Every hand of $5$ cards must …
- 28k
15
votes
Linear algebra proofs in combinatorics?
The Lindstrom-Gessel-Viennot Lemma uses the reflection principle on $S_n$ to say that the number of nonintersecting families of lattice paths in the plane equals the determinant of a matrix so that th …