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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
8
votes
1
answer
246
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The minimal number of partitions to cover all $k$ tuples
The set $N=\{1, 2, \ldots, 2k\}$ can be partitioned into pairs (e.g $(1,2),(3,4),\ldots,(2k-1,2k)$) in $\frac{(2k)!}{k!2^k}$ ways.
$k$-tuple is subset of size $k$ in $N$. We say that $k$-tuple is co …
5
votes
1
answer
456
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$(n-2)$-blocking sets in $AG(n,2)$
Let's define $k$-blocking set in affine space $AG(n,q)$ a set that meets every coset (translate of subspace) of dimension $k$.
I have seen a lot work related to minimal $(n-1)$-blockings set.
Cover …