Vandermonde sets and hyperovals
Combinatorics
2026-01-21 v1
Abstract
We consider relationships between Vandermonde sets and hyperovals. Hyperovals are Vandermonde sets, but, in general, Vandermonde sets are not hyperovals. We give necessary and sufficient conditions for a Vandermonde set to be a hyperoval. Therefore, we provide purely algebraic criteria for existence of hyperovals. Furthermore, we give necessary and sufficient conditions for the existence of hyperovals in terms of -functions, which can be considered as an analog of Glynn's Theorem for o-polynomials.
Keywords
Cite
@article{arxiv.1911.10798,
title = {Vandermonde sets and hyperovals},
author = {Kanat Abdukhalikov and Duy Ho},
journal= {arXiv preprint arXiv:1911.10798},
year = {2026}
}