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Results tagged with combinatorial-designs
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user 17581
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
votes
Best strategy for a combinatorial game
Let me address the case $k=N/2$. Consider a hypergraph whose edges are your groups. Then, basically, you are interested in the discrepancy of your hypergraph. The first estimate at the linked Wikipedi …
- 23.7k
3
votes
Accepted
Lower bound for a combinatorial problem ($N$ students taking $n$ exams)
My initial argument was erroneous. I'm rewriting everything completely.
Denote by $f(n)$ the maximal value of $N$ for that value of $n$. I claim that $$
f(k+\ell)\geq f(k)+f(\ell)+k \qquad\text{for …
- 23.7k
1
vote
Popular elements in cross-intersecting families
The answer is NO without any of the two additional assumptions.
Consider a set of $(t-1)^2$ elements $A=\{a_{ij}\}_{i,j=1}^{t-1}\subset[n]$. Let each $T_k$ contain a "row" $R_i=\{a_{ij}\}_{j=1}^{t-1} …
- 23.7k
1
vote
Accepted
On the existence of a certain graph/hypergraph pair
I'm sorry, but I do not understand why you cannot model the same example over a finite field.
Let, say, $V$ be the set of non-isotropic points in the projective space $P^3(\mathbb F_p)$ for a large $ …
- 23.7k