Bounds on sizes of general caps in $AG(n,q)$ via the Croot-Lev-Pach polynomial method
| Autor: | Bennett, Michael |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In 2016, Ellenberg and Gijswijt employed a method of Croot, Lev, and Pach to show that a maximal cap in $AG(n, q)$ has size $O(q^{cn})$ for some $c < 1$. In this paper, we show more generally that if $S$ is a subset of $AG(n, q)$ containing no $m$ points on any $(m - 2)$- flat, then $|S| < q^{c_mn}$ for some $c_m < 1$, as long as $q$ is odd or $m$ is even. Comment: 15 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|