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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. ...