Points below a parabola in affine planes of prime order

作     者：Adriaensen, Sam Weiner, Zsuzsa 

作者机构：Department of Mathematics and Data Science Vrije Universiteit Brussel Pleinlaan 2 Elsene1050 Belgium Department of Mathematical Sciences Worcester Polytechnic Institute 100 Institute Road WorcesterMA01605 United States HUN-REN-ELTE Geometric and Algebraic Combinatorics Research Group Pázmány Péter sétány 1/C BudapestH-1117 Hungary 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

摘      要：MSC Codes 51E15The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kiss and Somlai recently proved interesting properties of the set of points below the diagonal line. In this paper, we investigate the set of points lying below a parabola. We prove that in some sense, this set of points looks the same from all but two directions, despite having only one non-trivial automorphism. In addition, we study the sizes of these sets, and their intersection numbers with respect to lines. © 2024, CC BY.