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Jun
25
comment Comparing geodesics on a hypersphere
@AmitaiYuval maybe I misunderstood your comment, but I'm not interested in the distance between the two sets, rather I'm looking to see if the two paths moving along the hypercoordinates in the same way. I know that this is vague (hence the question), but imagine a normal two sphere: you can parameterize it by spherical coordinates $\phi, \psi$. Two arcs would be 100% similar if the change along the parametrized paths would invoke approximately the same change in these coordinates.
Jun
25
comment Comparing geodesics on a hypersphere
@AmitaiYuval there is absolutely no guarantee that they intersect, in fact most of them don't.
Jun
2
comment Spare storage of a tree
Perfect! I was looking for a labeling like this! I knew there was some $N$ at which you couldn't store a tree using a single 64-bit integer -- obviously there are an infinite such trees.
Jun
2
comment Spare storage of a tree
@Gamamal even for connected graphs, isn't every tree a spanning tree to some graph? For example, shouldn't every tree be a spanning tree to the complete graph?
Jun
2
comment Spare storage of a tree
@Gamamal there was no restriction that the graph had to be connected, thus a spanning tree might not exist.
Jun
2
comment Spare storage of a tree
This question may be more suited for one of the CS SE's, if you agree let me know and I can close and repost.
Apr
25
comment What is a $0\times0$ or $0\times3$ matrix?
@DavidH Since this question has been around for awhile, do you want to write up your comment as an answer? I'll accept it if you do and essentially close this question.
Apr
20
comment Percolation over the integers
I'm unsure why I this question has both a favorite (STAR) and a downvote. If the question is poor, please let me know how to improve it or provide some additional feedback!
Mar
5
comment “The Egg:” Bizarre behavior of the roots of a family of polynomials.
@Stephen Look at the dates posted. The answer by myself and Gottfried Helms against the above post are about two years apart. There is often a correlation between delayed answers and score (though not always).
Feb
14
comment What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?
I'm not sure what you are looking for in an answer. I'm giving you a couple of really neat cutting edge problems concerning transportation, but it is sometimes surprising that linear programming can handle such large problems in practice.
Sep
12
comment Bitcoin math problem example
Also bitcoin.stackexchange.com
Sep
3
comment Is there anything special about a graph with the golden ratio in its spectrum?
Can provide a reference for "experimental evidence indicates that most graphs have characteristic polynomial irreducible over the rationals"?
Sep
1
comment Is there anything special about a graph with the golden ratio in its spectrum?
Right, that explains why they are relatively common. I was interested if the graphs themselves have any special symmetry. For example, none of the graphs seem particularly dense (in that they are planar or nearly so). These seems to be true for the graphs of order 7 that I examined as well.
Aug
7
comment How many distinct chromatic polynomials are there for simple connected graphs?
@jp26 I am looking for the number of unique polynomials not the number of unique graphs. I just realized that the title and the text contradict each other. I'll make an edit to correct this. However, the other question is very interesting too and worth asking in it's own right.
Aug
6
comment How many distinct chromatic polynomials are there for simple connected graphs?
@jp26 I agree! I was only waiting a few days before I accepted the answer to see if someone could come up with a reference with a longer set of terms. Independently I've computed this up to n=10 (without using Sage), so I'll post it as an answer if no one else does.
Jun
25
comment The expected outcome of a random game of chess?
Two suggestions though, the actual counts used by the simulations and a two sided p-value. Since you are much, much closer to 1/2, it be interesting to see what the statistics say. "perfectly consistent" is not quite precise enough!
Jun
25
comment The expected outcome of a random game of chess?
Nice catch, chalk this one up to the power of peer review! To be honest, this library was simply the easiest to install and get up and running, I imagine that a C library may be much faster to run long simulations. Also, mate is possible with two moves.
Jun
25
comment The expected outcome of a random game of chess?
@nbubis I'm going to let Winther take the credit for finding the flaw in the code above. I happy enough, my initial answer, flawed as it was, was enough to spur a better investigation. I'll update my answer and point to his, IMHO he answers the question correct and should get the check.
Apr
13
comment Forbidden toroidal minors
Wow, that is a much larger set than I expected! Do you know, off-hand, if there are simple ways to test if a graph is toroidal? If not, I can ask in a new question.
Apr
2
comment Fourier decomposition of the Mandelbrot set
Thanks for the article!