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Dec
19
awarded  Popular Question
Dec
19
comment Proofs without words
go ahead.......
Dec
19
comment randomness in nature
Too bad. Greg could give a beautiful and useful answer.
Dec
19
answered Proofs without words
Dec
19
comment randomness in nature
It is certainly not a typical MO question (and should not be), but I think this type of question should be welcomed in MO (and by mathematicians, in general).
Dec
19
awarded  Enlightened
Dec
19
awarded  Nice Answer
Dec
19
answered randomness in nature
Dec
19
comment What precisely Is “Categorification”?
Very nice answers. Anything more to say, to edit, to polish, to link?
Dec
19
comment Generalizations of Planar Graphs
More answers, remarks, links are most welcome. In particular: links to connections between planar graphs and commutative algebra (and other algebra), some info on the simlicial complex of (edges of) planar graphs on n vertices, some interesting extensions of planar graphs related to the 4CT.
Dec
19
answered Generalizations of Planar Graphs
Dec
18
revised Fundamental Examples
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Dec
18
revised Fundamental Examples
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Dec
18
revised Fundamental Examples
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Dec
16
revised The density hex
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Dec
16
revised The density hex
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Dec
16
comment The density hex
Anyway, it is a very nice problem and the connection to Gales theorem that Harrison found is also great.
Dec
15
comment The density hex
Yes, your graph seems intermediate one between G_\infty considered by BKLO and G_1 considered by AK; and your question for G_1 is also interesting and does not seem to be known (and also for the specific graph you study).
Dec
15
revised The density hex
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Dec
14
comment The density hex
I think we can expect for n fixed (say n=3) and d large a simpler combinatorial proof with much better bounds. anyway I think the results on separating all cycles in [0,1]^n and their discrete analogues are relevant. Look here (and the links there) :gilkalai.wordpress.com/2009/05/27/…