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Geometric combinatorics in discrete settings
(University of Missouri--Columbia, 2011)
This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog ...
Finite point configurations and projection theorems in vector spaces over finite fields
(University of Missouri--Columbia, 2010)
We study a variety of combinatorial distance and dot product related problems in vector spaces over finite fields. First, we focus on the generation of the Special Linear Group whose elements belong to a finite field with ...