Katona Gyula:
Constructing union-free pairs of k-element subsets
<br><br>
Consider pairs of disjoint k-element subsets of an n-element set.
We want to choose many such pairs in such a way, that each k-element
set
is used at most once
and the unions of the pairs are all different. It will be proved that
the trivial upper bound
(integer part of the half of the total number of k-element subsets) can
be reached.