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Erdős distance problem in the hyperbolic half-plane
(University of Missouri--Columbia, 2009)
The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ...
Explorations of geometric combinatorics in vector spaces over finite fields
(University of Missouri--Columbia, 2008)
We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ...
Extension theorems in vector spaces over finite fields
(University of Missouri--Columbia, 2008)
We study the L[superscript p] - L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ...