Fixee
Reputation
5,923
Top tag
Next privilege 10,000 Rep.
Access moderator tools
 Aug5 comment Expected length of a sequence that contains all words of a given length. @ByronSchmuland I think that's the same ref leonbloy cited at the end of his answer below. Aug5 revised Determine whether the argument is valid or invalid typesetting cleanup Aug5 answered Determine whether the argument is valid or invalid Aug4 comment N white and black balls and N boxes Probability Given $N$ new users posting $N$ new questions which are worded as demands rather than questions, what is the probability they are all homework problems? Jul17 awarded Popular Question Jun29 comment Fibonacci sequence - how to prove $a_n=\frac{1}{\sqrt{5}} ((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)$ without induction This is given as a warmup in the free text by Wilf called generatingfunctionology. Jun28 comment How to find generator in a finite group?what is generator? When I said, "suppose you can factor" the "you" is the OP who is (presumably) a human trying to solve a problem. I did not (and would not) say "suppose a factorization exists for $(p-1)$". Jun28 answered How to find generator in a finite group?what is generator? Jun25 awarded Informed Jun24 comment practical arithmetic in prime factorizations Ross, I don't get your answer. You seem to be reiterating his idea rather than answering his question regarding the use of this technique in actual software. Jun24 revised practical arithmetic in prime factorizations added 91 characters in body Jun24 answered practical arithmetic in prime factorizations Jun16 revised How many expected people needed until 3 share a birthday? added 208 characters in body Jun15 revised Probability (usage of recursion) added 325 characters in body Jun15 revised Probability (usage of recursion) added 325 characters in body Jun15 answered Probability (usage of recursion) Jun15 comment How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$? @PeterR: Often mathematicians will use "elementary" to mean "does not use complex analysis". As you can see, "elementary" does not mean "easy." Jun15 comment Conjecture: The following sum is asymptotic to $\sqrt{9πm/8}$ Interesting. This immediately gives that three collisions occur in less than an expected $2 \sqrt{\pi m/2} = \sqrt{2\pi m}$. (In fact, I will guess that it's $15/8 \sqrt{\pi m/2}$.) Since $\sqrt{2\pi m}$ is the square root of the circumference of a circle of radius $m$, there is clearly a geometric proof we're missing. :) Jun15 comment How many even number in a sequence are there? Your iff is false in both directions. Jun15 comment Second pair of matching birthdays @ShreevatsaR: The reason my simulation made me believe the answer was not proportional to $\sqrt{M}$ was that--as your program shows--the multiplier starts above 2.1 and gradually settles to 1.88... But your argument in your answer that it must be a multiple of $\sqrt{M}$ is quite convincing.