Name
Abstract | ||
|---|---|---|
We prove that the number of directions contained in a set of the form AxB subset of AG(2,p), where p is prime, is at least vertical bar A vertical bar vertical bar B vertical bar-min{vertical bar A vertical bar; vertical bar B vertical bar}+2. Here A and B are subsets of GF (p) each with at least two elements and vertical bar A vertical bar vertical bar B vertical bar<p. This bound is tight for an infinite class of examples. Our main tool is the use of the Redei polynomial with Szonyi's extension. As an application of our main result, we obtain an upper bound on the clique number of a Paley graph, matching the current best bound obtained recently by Hanson and Petridis. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s00493-020-4516-z | COMBINATORICA |
DocType | Volume | Issue |
Journal | 41 | 6 |
ISSN | Citations | PageRank |
0209-9683 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Di Benedetto Daniel | 1 | 0 | 0.34 |
| Solymosi Jozsef | 2 | 0 | 0.34 |
| Ethan P. White | 3 | 5 | 3.15 |