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bio website jamespropp.org
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visits member for 4 years, 10 months
seen Nov 21 at 20:49

I am interested in combinatorics, probability, dynamical systems, and various other topics.


Nov
14
accepted Origin of the numbers game
Nov
14
comment Origin of the numbers game
I hear that Knuth studied it as well; can anyone provide a pointer to Knuth's article?
Nov
13
asked Origin of the numbers game
Nov
12
comment Isotropy of Apollonian disk-packing
You are completely right! My bad for assuming Hee was a he.
Nov
12
revised Isotropy of Apollonian disk-packing
I corrected a few typos
Nov
11
answered Isotropy of Apollonian disk-packing
Nov
11
comment Isotropy of Apollonian disk-packing
@Hao Chen: The work of Hee Oh is very relevant; thanks for the suggestion! I recommend the slides at gauss.math.yale.edu/~ho2/extendedICM.pdf ; they are well-written and the pictures are both pleasurable and informative.
Nov
11
awarded  Socratic
Nov
10
revised Spirals in Apollonian circle-packings
Added forward pointer to follow-up question
Nov
10
asked Three-dimensional Apollonian spirals
Nov
8
awarded  Good Question
Nov
5
comment Spirals in Apollonian circle-packings
I like Noam's argument. Can anyone complete the proof by showing that the angle in question is irrational?
Nov
5
comment Spirals in Apollonian circle-packings
I should point out a subtlety that some readers may have missed: conformal maps are only locally angle-preserving, so the angular distribution of the unit vectors in the general case cannot be obtained by applying a rotation or other simple map to the unit vectors in the special case that Noam proposes. However, since the points $P_n$ and $Q_n$ all approach $P_{\infty}$, and since the inversive map preserves angles in the vicinity of $P_{\infty}$, we can ignore this distortion for purposes of the asymptotic angular distribution of the vectors.
Nov
4
accepted Bijective proof of an Abel-Hurwitz-type identity
Nov
4
comment Bijective proof of an Abel-Hurwitz-type identity
That's a nice style of argument (and it helps me get a better feel for Postnikov's point of view). Thanks for explaining it to me. (By the way, I think Sunday's meeting was officially reckoned as the 60th meeting of the Cambridge Combinatorics and Coffee Club, not the 61st; not that it matters.)
Nov
4
comment Bijective proof of an Abel-Hurwitz-type identity
Yes, it's $n^{n-2}$.
Nov
4
asked Bijective proof of an Abel-Hurwitz-type identity
Nov
3
asked Spirals in Apollonian circle-packings
Oct
15
asked Isotropy of Apollonian disk-packing
Oct
14
awarded  Nice Question