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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 views

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 …
Ashot's user avatar
  • 337
5 votes
1 answer
456 views

$(n-2)$-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 …
Ashot's user avatar
  • 337