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Results tagged with combinatorial-designs
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user 29873
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.
2
votes
2
answers
293
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Resolvable designs from projective space
Resolvable designs are block designs with the additional property that the blocks can be partitioned into partitions of the points. It is easy to see that lines in affine space form a resolvable desi …
- 7,633
9
votes
1
answer
530
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Does $(\mathbb{Z}/n\mathbb{Z})^2$ ever admit a difference set when $n$ is odd?
A difference set of a group $G$ is a subset $D\subseteq G$ with the property that there exists an integer $\lambda>0$ such that for every non-identity member $g$ of $G$, there exist exactly $\lambda$ …
- 7,633
1
vote
0
answers
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Are sharper lower bounds known for these potentials on the sphere?
Fix a positive integer $\ell$. For $x_1,\dotsc,x_n\in S^{d-1}$, Venkov proved that
$$
\sum_{i=1}^n\sum_{j=1}^n(x_i\cdot x_j)^{2\ell}\geq\frac{(2\ell-1)!!(d-2)!!}{(d+2\ell-2)!!}\cdot n^2,
$$
with equal …
- 7,633