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- W4387210485 abstract "The relational complexity of a subgroup $G$ of $mathrm{Sym}(Omega)$ is a measure of the way in which the orbits of $G$ on $Omega^k$ for various $k$ determine the original action of $G$. Very few precise values of relational complexity are known. This paper determines the exact relational complexity of all groups lying between $mathrm{PSL}_{n}(mathbb{F})$ and $mathrm{PGL}_{n}(mathbb{F})$, for an arbitrary field $mathbb{F}$, acting on the set of $1$-dimensional subspaces of $mathbb{F}^n$. We also bound the relational complexity of all groups lying between $mathrm{PSL}_{n}(q)$ and $mathrm{P}Gammamathrm{L}_{n}(q)$, and generalise these results to the action on $m$-spaces for $m ge 1$." @default.
- W4387210485 created "2023-10-01" @default.
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- W4387210485 date "2023-09-27" @default.
- W4387210485 modified "2023-10-01" @default.
- W4387210485 title "The relational complexity of linear groups acting on subspaces" @default.
- W4387210485 doi "https://doi.org/10.48550/arxiv.2309.16111" @default.
- W4387210485 hasPublicationYear "2023" @default.
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