Craig
Reputation
1,797
Top tag
Next privilege 2,000 Rep.
 Dec 29 awarded Nice Question Oct 14 awarded Revival Aug 30 awarded Yearling Sep 30 awarded Explainer Aug 30 awarded Yearling Dec 5 awarded Taxonomist Aug 30 awarded Yearling Oct 7 awarded Nice Question Aug 30 awarded Yearling Dec 20 comment Algorithm for scrolling through different orbits in a permutation group @JoelCohen, you are slightly off on your description of $C_\pi$. Specifically, $C_\pi$ also contains those permutations which map equal-sized cycles in $\pi$ to each other. For example, the centralizer of $(1,2)(3,4)$ in $S_4$ contains $(1,3)(2,4)$. I believe this does give you a full list of generators of $C_\pi$ -- 1) cycles in $\pi$, 2) permutations of the fixed points of $\pi$, and 3) order-preserving swaps of the cycles of a given size in $\pi$. I might be missing something though regarding more complicated actions within each cycle of a given size. Dec 16 answered Expectation of function of random variable? Dec 15 comment Problem about the sum of independent exponential variable i.i.d., centered and has variance 1. The results then follow from the Central Limit Theorem. Of course, this is an approximation that only holds for large $n$... Dec 9 answered Theorem for a $2$-dimensional (easy) integral with variable boundary Nov 29 comment How is a Halton sequence related to a Latin hypercube? Another drawback of both techniques is whenever you want to look at multi-point correlations -- both techniques don't let the points cluster as much as a truly random selection would. I believe the Halton sequence does better. Nov 15 comment Planar kelvin problem I think you got the maximal side length wrong. If the side of the hexagon is $s$, the area is $A = 3\sqrt{3}s^2/2$, so the maximal sidelength is $\sqrt{2A/3\sqrt{3}}$. Nov 15 answered Exciting games and material to motivate children to math Nov 15 answered A subtle modification to the $t$ distribution Nov 8 answered $\sin(A)$, where $A$ is a matrix Nov 7 comment A function of two functions that loses dependence on an argument Formally, $h$ does require $u$, as the product on the right hand side is undefined when $u=0$. Nov 6 comment Solve $\displaystyle\int_{0}^a \left(3^{\frac{1}{3} \left( x^3 - 3x \right) }-1\right)\, dx = 0$ using elementary methods Are you trying to solve for $a$? In that case the only answer is $a=0$, since $3^z$ is positive for all real $z$.