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Mar 11, 2010 at 9:25 history edited Douglas S. Stones CC BY-SA 2.5
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Mar 10, 2010 at 6:40 history edited Douglas S. Stones CC BY-SA 2.5
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Mar 6, 2010 at 21:18 vote accept miforbes
Mar 6, 2010 at 21:18 comment added miforbes I suppose the remains of the question are too open-ended, so I'll mark this answer as the one I'm happy with. As for the c=n-1 case, I would imagine that for all $P$, $N(P)\equiv 0\mod 2$, but don't have any good reason to think this. However, I'm really looking for $c=\omega(n)$, (see my expanded section on the original motivation), so the $c=n-1$ case is slightly less interesting to me.
Mar 6, 2010 at 21:01 comment added miforbes Ah, this seems to answer the most well-defined aspect of my question, though I'll have to take some more time later to fully digest this. I'm not sure if I should mark my question as "answered" as I'll comment more on the broader question I have.
Mar 6, 2010 at 10:55 history edited Douglas S. Stones CC BY-SA 2.5
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Mar 6, 2010 at 10:41 history edited Douglas S. Stones CC BY-SA 2.5
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Mar 6, 2010 at 10:34 history answered Douglas S. Stones CC BY-SA 2.5