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In this thesis we study a number of problems in Discrete Combinatorial Geometry in finite spaces. The contents in this thesis are structured as follows: In Chapter 1 we will state the main results and the notations which will be used throughout the thesis. ...
Let G = (V, E) be an (n, d, lambda)-graph. In this paper, we give an asymptotically tight condition on the size of U subset of V such that the number of paths of length k in U is close to the expected number for arbitrary integer k >= 1. More precisely, we ...
Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...