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This thesis includes several results on the extremal combinatorics ofhyperplane arrangements, kinetic point sets, and other geometric struc-tures. It consists of three papers published or submitted elsewhere. “ABichromatic Incidence Bound and an Application”, joint with GeorgePurdy and Justin Smith, was published in Discrete and ComputationalGeometry. I presented “Collinearities in Kinetic Point Sets”, joint withGeorge Purdy, Justin Smith, and Csaba T¿¿¿¿th, at the 23rd Canadian Con-oference on Computational Geometry, 2011. “Some Results Related to aConjecture of Dirac’s”, joint with George Purdy and Justin Smith, hasbeen submitted to The Electronic Journal of Combinatorics. |
