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Maximal point sets on discrete toric grid with no three colinear points
 Skotnica, Michael ; Tancer, Martin (advisor) ; Kala, Vítězslav (referee)
Let τ(Tm×n) denote maximal number of points on a discrete toric grid of the sizes m×n with no three colinear points. This thesis examines τ(Tm×n) for various m, n. It is a variant of the well-known no-three-in-line-problem. First, we present some previously known results. Then we generalize them in various directions. In particular we improve upper and lower bounds for cases which have not been solved in previous papers especially for cases when the sizes of the grid are prime powers. At the end we define the sequence (τ(Tm×n))n∈N and we prove that it is periodic for all fixed m. 1
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