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April 9th, 2019, 01:19 PM   #1
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Joined: Apr 2019
From: North Carolina

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Question Arrangements of Hyperplanes

There are eight possible arrangements of three planes in which any two planes either intersect in a line, coincide, or are parallel. I've been trying to determine the number of similar arrangements of four hyperplanes in 4-space, mainly by analyzing the corresponding coefficient and augmented matrices for four equations, four unknowns. I feel like I'm starting to get there, but not sure I can do it. Can anyone give me some ideas?

Ultimately, I'd like to find the number of similar arrangements of n hyperplanes in n-space.

Look forward to any responses!
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