# Journal article

## On sets defining few ordinary lines

Abstract:

Let P be a set of n points in the plane, not all on a line. We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two points of P. This confirms, for large n, a conjecture of Dirac and Motzkin. In fact we describe the exact extremisers for this problem, as well as all sets having fewer than n - C ordinary lines for some absolute constant C. We also solve, for large n, the "orchard-planting problem", which asks for the maximum numbe...

### Authors

Publication date:
2012-08-23
Keywords:
Pubs id:
pubs:398457
UUID:
uuid:67db1685-907b-4c2a-afd5-f871453fd89c
Local pid:
pubs:398457
Source identifiers:
398457
Deposit date:
2013-11-16