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 Sep30 awarded Explainer Aug30 awarded Yearling Dec5 awarded Taxonomist Aug30 awarded Yearling Oct7 awarded Nice Question Aug30 awarded Yearling Dec20 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. Dec16 answered Expectation of function of random variable? Dec15 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 $n$... Dec9 answered Theorem for a $2$-dimensional (easy) integral with variable boundary Nov29 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. Nov15 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 $\sqrt{2A/3\sqrt{3}}$. Nov15 answered Exciting games and material to motivate children to math Nov15 answered A subtle modification to the $t$ distribution Nov8 answered $\sin(A)$, where $A$ is a matrix Nov7 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 $u=0$. Nov6 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 $z$. Nov4 comment Probability question: optimal strategy @RossMillikan: That's an unstable equilibrium, as each is indifferent between firing at time $x^*$ and not firing, knowing that the other one will. Nov4 comment Probability question: optimal strategy Ross, there is one issue -- if A does not fire at this time $x^*$, B doesn't know what A's $\Delta t$ is, so he can't fire at $x^* + \Delta t/2$. This is why I think both adopt a mixed strategy. Nov4 comment Probability question: optimal strategy My suspicion is that the correct answer is a mixed strategy. Each has some probability distribution of when they will shoot given that the other has not yet shot. Now how to determine said distribution... I'm still thinking about it.