The number of k-intersections of an intersecting family of r-sets
| dc.creator | Talbot, John | |
| dc.date | 2003-06-06 | |
| dc.date.accessioned | 2026-07-07T04:58:38Z | |
| dc.date.available | 2026-07-07T04:58:38Z | |
| dc.description | 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. | |
| dc.description | 10 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0306119 | |
| dc.identifier | http://arxiv.org/abs/math/0306119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67720 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D05 | |
| dc.title | The number of k-intersections of an intersecting family of r-sets | |
| dc.type | text |