Lacunary polynomials over finite fields and their applications
Jozsef Solymosi, Kyle Chi Hoi Yip and Ethan White (University of British Columbia)
Abstract: In the early 70's Laszlo Redei published a book titled "Lacunary Polynomials Over Finite Fields". In Redei's notation a polynomial $f(x)$ is lacunary if there is a gap between its largest and second largest exponent. For example $x^5-2x+1$ is a lacunary polynomial. His book is about the properties and applications of lacunary polynomials. His most important application is bounding the number of directions determined by point sets in an affine Galois plane. We revisit his work giving better bounds on the number of directions determined by a Cartesian product. As an immediate corollary we give an upper bound on the clique number of a Paley graph. After the intro (by Jozsef Solymosi) Kyle Yip will talk about the Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields and then Ethan White will talk about the number of distinct roots of a lacunary polynomial over finite fields.
combinatorics
Audience: researchers in the topic
Carleton Combinatorics Meeting 2021
Series comments: See the external webpage for more details: people.math.carleton.ca/~dthomson/CCM2021
To contact, please use CCM2021@math.carleton.ca and prefix your subject with "[CCM2021-request]"
| Organizers: | Daniel Panario, David Thomson*, Qiang Wang |
| *contact for this listing |