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A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?
Published online by Cambridge University Press: 01 September 2009
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.)
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- Information
- Combinatorics, Probability and Computing , Volume 18 , Issue 5: New Directions in Algorithms, Combinatorics and Optimization , September 2009 , pp. 691 - 705
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- Copyright © Cambridge University Press 2009
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