On Diameters of Cayley Graphs over Matrix Groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913570152775680 |
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| author | Porat, Eitan |
| author_facet | Porat, Eitan |
| contents | 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 $C>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Diameters of Cayley Graphs over Matrix Groups Porat, Eitan Combinatorics 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 $C>0$. |
| title | On Diameters of Cayley Graphs over Matrix Groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.06929 |