A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?
- 1 September 2009
- journal article
- research article
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 18 (5) , 691-705
Abstract
We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)Keywords
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