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seen Jan 15 '13 at 14:31

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comment Stable singularities of smooth map $\mathbb R^3\to \mathbb R^4$
B. Morin: Formes canoniques des singularités d'une application différentiable, Comp. Rend. Acad. Sci. Paris 260 (1965), pp. 5662-5665 should have it
Jul
13
answered Stable singularities of smooth map $\mathbb R^3\to \mathbb R^4$
Jan
5
comment Limit of a sequence of polygons.
Just a little error: there are no angles in the limit curve. It is composed of self-similar arcs under some affine transformations (with a linear part with matrix entries 1/3, 1/3, 0, 1/3, say), which are not similarities, so no nontrivial angles can be present.
Dec
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awarded  Yearling
Aug
19
answered Probability of Outcomes Algorithm
Aug
2
comment In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
@Casebash: the binary one.
Jul
19
answered Smallest area shape that covers all unit length curve
Jul
14
comment In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
To answer "is it always possible to construct a set of cycle bases with each and every edge shared by at most 2 bases?" in the negative, I construct a graph for which no such cycle base exists. The example I give is the complete graph on 7 vertices. In it, the cycle space (see above) has dimension #edges-#vertices+1=21-7+1=15. No matter how you select 15 nonempty cycles or unions of cycles, those will have at least 45 edges counted with multiplicity. This is more than twice the number of edges in the graph, so by the pigeonhole principle at least one edge will be used 3 times or more.
Jul
8
comment In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
I answer the question "In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?" in the negative, so one counterexample is all it takes. If you wanted to ask a more precise question, then BS's lead is what you should read. As for your other question, please consult en.wikipedia.org/wiki/Cycle_space .
Jul
7
comment In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
en.wikipedia.org/wiki/Mac_Lane%27s_planarity_criterion says: S. Mac Lane, A combinatorial condition for planar graphs, Fund. Math. 28 (1937), 22–32.
Jul
7
comment In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
I implicitly use that all cycles contain at least 3 edges, and that the dimension of the cycle space is the number of edges exceeding that of a tree with the same vertices. Both facts are straightforward, could you please elaborate on where exactly you have problems?
Jul
6
answered In a graph, is it always possible to construct a set of cycle bases, with each and every edge Is shared by at most 2 cycle bases?
Jun
29
revised Binary Sequences of Length 2n
added clarification
Jun
29
answered Binary Sequences of Length 2n
Jun
18
comment Probability of a Point on a Unit Sphere lying within a Cube
What kind of accuracy are you aiming for? Approximating the surface measure of the sphere by a standard Gaussian would give results not worse than deviating ~1/n^{1/2} in d, and would probably be much better than that in most cases.