Gil Kalai
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 Dec 5 comment Chances to win an election if you ask what is the probability that B wins and still from a random poll of 1100 voters 750 vote A and 250 B the answer is 0. It is true that people change their minds and also that polls are not entirely reliable. Fot the question you asked even under realistic scenario I would regard 1 as the best answer. Dec 5 comment Chances to win an election much much much much much higher. I would simply say 1. Dec 5 answered Sum of $n$ vectors in $(\mathbb Z/n)^k$ Dec 5 comment Is there a high-concept explanation for why characteristic 2 is special? I wonder if you have any insight or conceptual explanation for why odd order groups are all solvable. Dec 5 answered Generalizations of the Birkhoff-von Neumann Theorem Dec 5 awarded Enthusiast Dec 4 awarded Nice Question Dec 4 comment Generalizations of Planar Graphs (This is because of the wonderful Pandora box oppened by Mike Freedman :) ) Dec 4 comment Generalizations of Planar Graphs Dear Joe, This refer to an important extension of planar graphs: Graphs that can be drawn in the plane by Jordan curves so that there are no r edges that every pair cross. For r=2 these are planar graphs and for r=3 these are the quasi-planar graphs in the linked paper. It is expected but not knwon that for larger r there is a linear bound on the number of edges. Dec 4 comment What is an integrable system Very good answers! I'd love to see more angles to this important issue, which is why a little bounty is offered. Dec 4 comment Generalizations of the Birkhoff-von Neumann Theorem These are all very nice answers. To encourage more I start a little bounty where as before I will "accept" one useful answer. Dec 4 comment Why are planar graphs so exceptional? A follow up question which gives also a wide context for Harrison's question is here mathoverflow.net/questions/7650/… A follow up blog discussion is here gilkalai.wordpress.com/2009/12/03/… Dec 4 comment Generalizations of Planar Graphs One generalization that Kristal point out to is graphs that can be embedded in a given surface. This is perhaps the most studied generalization of planar graphs. Going to higher dimensional objects was suggested by Alon (embeddability of k spaces into R^2k.) Kristal's suggestion to replace the ambient space by other spaces is certainly interesting. If I remember correctly embeddability of k manifolds in Euleriam 2k-manifolds (2k-manifolds with Euler characteristic 2) is equivalent to embeddability in R^{2k}. (OK, maybe the condition is vanishing middle homology and not being Eulerian.) Dec 4 comment Generalizations of Planar Graphs That's a very nice idea! Dec 4 revised Why are planar graphs so exceptional? grammer Dec 3 comment Generalizations of Planar Graphs I think that embeddability of 2 dimensional spaces into R^4 is the most difficult case. Dec 3 comment Generalizations of Planar Graphs Muktiple answers/posts are welcomed. I hope we can have a useful source. Dec 3 comment Generalizations of Planar Graphs Dear Alon, this is a very important and interesting generalization. Dec 3 revised Generalizations of Planar Graphs deleted 12 characters in body Dec 3 asked Generalizations of Planar Graphs