On Diameters of Cayley Graphs over Matrix Groups

Autor:	Porat, Eitan
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We establish for the matrix group $G=\mathrm{SL}_{n}\left(\mathbb{F}_{p}\right)$ that there exist absolute constants $c\in\left(0,1\right)$ and $C>0$ such that any symmetric generating set $A$, with $\left|A\right|\geq\left|G\right|^{1-c}$ has a covering number $\leq Cn^{2}.$ This result is sharp up to the value of the constant $C>0$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.06929 Zobrazit plný text záznamu View this record from Arxiv