UBC Discrete Math Seminar: Kyle Yip

In this talk, we will discuss how to improve the trivial upper bound on the clique number of Paley graphs and generalized Paley graphs using a different method. I will revisit the direction set determined by a Cartesian product in an affine Galois plane $AG(2,q)$ and show that most Cartesian products determine many directions. The main result we obtained is: for any positive function $h$ such that $h(x)=o(x)$ as $x \to \infty$, $\omega(P(q,d)) \leq \sqrt{q}-h(p)$ for almost all non-squares $q$.