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Jan 4, 2022 at 2:14 comment added Jeremy Martin Not a reference or a solution, just an observation: since there is probably some matroid or matroid-like structure floating around that has to be uniform. For line arrangements this would be precisely the matroid represented by vectors spanning the lines; for $d>1$ maybe you can do something with exterior products. This could be a way to produce some bounds (not necessarily sharp). Interesting problem.
Dec 23, 2021 at 18:25 comment added Nick Salter @ArB - not necessarily. I've noticed in practice, however, that it is often possible to choose the $A_\sigma$ so that it is.
Dec 23, 2021 at 18:17 comment added ArB Do you want $\sigma \mapsto A_\sigma$ to be a group homomorphism?
Dec 23, 2021 at 16:34 history edited Nick Salter CC BY-SA 4.0
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Dec 23, 2021 at 16:22 history asked Nick Salter CC BY-SA 4.0