| We will be examining a number of extremal problems in combinatorial geometry where our ambient space is a vector space over a finite field. In particular, we try to answer the question "How many points can a subset of F dq have so that the points in the subset do not determine X," where X is a given geometric configuration.;The constructs we examine will include the following: 1. k-simplices: Unordered (k + 1)-tuples of points in Fd q in which the distances between every pair of points is predetermined. 2. k-chains: Ordered (k + 1)-tuples of points in Fdq in which the distances between consecutive pairs of points is predetermined. 3. Spread: A finite field analog of angle measure. |
