15 citations · 86 across the 50 of their papers we have counts for
4 papers · 1 filter
Incompatible intersection properties
Peter Frankl, Andrey Kupavskii
Let be a family in which any three sets have non-empty intersection and any two sets have at least elements in common. The nearly best possible bou…
A stability theorem on cube tessellations
Peter Frankl, Janos Pach
It is shown that if a -dimensional cube is decomposed into n cubes, the side lengths of which belong to the interval n$ is a perfec…
The Erdős Matching Conjecture and concentration inequalities
Peter Frankl, Andrey Kupavskii
More than 50 years ago, Erd\H os asked the following question: what is the maximum size of a family of -element subsets of an -element set if it has no pai…
New inequalities for families without k pairwise disjoint members
Peter Frankl, Andrey Kupavskii
Some best possible inequalities are established for k-partition-free families (cf. Definition 1) and they are applied to prove a sharpening of a classical result of Kleitman concer…