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Jun 7, 2018 at 2:34 comment added Hempelicious Thank you for your answer! I think I fully understand how this works now. Do you want to post a similar answer on math.SE? I could also post my understanding of your answer there. Again, thanks!
Jun 7, 2018 at 2:33 vote accept Hempelicious
May 31, 2018 at 23:23 comment added Jeremy Brazas You don't have to exclude $n=1$...I guess it's a preference. But the argument absolutely requires the form above for $n\geq 2$. Why would you want to consider $n=1$ as something special when you don't have to? My instinct to start with $n\geq 3$ is related to covers of simplicial complexes...that is all.
May 31, 2018 at 18:52 comment added Steve D Right, I think I followed the argument, but then seeing this requirement made me second-guess it. Sure, we can always refine, but my question was more "why do we have to?"
May 31, 2018 at 18:38 comment added Jeremy Brazas @SteveD Well, $n= 2$ could be included for this particular proof but this is not really an important feature. You could always take finer partitions and consider only sets of the form given where $n$ is greater than some fixed number. Allowing $n=1$ would just require an unnecessary extra case to write.
May 31, 2018 at 17:57 comment added Steve D Why do we need $n\ge3$?
May 29, 2018 at 21:49 history edited Jeremy Brazas CC BY-SA 4.0
added 52 characters in body
May 29, 2018 at 19:59 history answered Jeremy Brazas CC BY-SA 4.0