bio | website | gilkalai.wordpress.com |
---|---|---|
location | Jerusalem | |
age | 59 | |
visits | member for | 5 years, 2 months |
seen | 12 hours ago | |
stats | profile views | 17,392 |
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University
Dec 6 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Generalizations of Planar Graphs
(This is because of the wonderful Pandora box oppened by Mike Freedman :) ) |
Dec 4 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Generalizations of Planar Graphs
That's a very nice idea! |
Dec 4 |
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Why are planar graphs so exceptional?
grammer |
Dec 3 |
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Generalizations of Planar Graphs
I think that embeddability of 2 dimensional spaces into R^4 is the most difficult case. |