9,366 reputation
11115197
bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 2 months
seen 12 hours ago
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Dec
6
comment most general way to generate pairwise independent random variables?
There is a large body of literature on constructions of k-wise independent random variables. I suggest to look at Alon and Spencer's book on the probabilistic method.
Dec
6
revised books well-motivated with explicit examples
edited tags
Dec
6
revised Fundamental Examples
added 173 characters in body
Dec
6
comment Fundamental Examples
A very nice example. It is true that the examples vary in terms of importance and also in terms of how large we understand the concept of an "example".
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.