Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of k-intersections of an intersecting family of r-sets   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.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph