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April 9th, 2019, 01:19 PM  #1 
Newbie Joined: Apr 2019 From: North Carolina Posts: 2 Thanks: 0  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 4space, 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 nspace. Look forward to any responses! 

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