The number of k-intersections of an intersecting family of r-sets

Details The number of k-intersections of an intersecting family of r-sets The number of k-intersections of an intersecting family of r-sets

2003-06-06

arxiv.org/abs/math/0306119v1

Mathematics

Combinatorics

10 pages, 1 figure

Scientific paper

The Erdos-Ko-Rado theorem tells us how large an intersecting family of r-sets from an n-set can be, while results due to Lovasz and Tuza give bounds on the number of singletons that can occur as pairwise intersections of sets from such a family. We consider a natural generalization of these problems. Given an intersecting family of r-sets from an n-set and 1\leq k \leq r, how many k-sets can occur as pairwise intersections of sets from the family? For k=r and k=1 this reduces to the problems described above. We answer this question exactly for all values of k and r, when n is sufficiently large. We also characterize the extremal families.

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