@Ilya I used the Poisson boundary and understood it from an ergodic/measure-theoretic perspective which was sufficient for my needs. I don't have a lot of probabilistic intuition about it, if any at all.
@tb: but what do you call an ergodic perspective? Doesn't it imply thinking of measurable maps (which is equivalent to a discrete-time Markov process)?
@Ilya In fact I think about it as the action of $\mathbb{N}$ or $\mathbb{Z}$ which of course is equivalent to a Markov process but that don't impress me much nor help me much with my understanding.
@tb I proved an already known result in an answer to a question on sci.math. It counts the number of walks of length 2n that stay on one side of the origin and return to the origin
there are obviously $\binom{2n}{n}$ walks of length $2n$ ($n$ "$+1$"s and $n$ "$-1$"s)
and there are exactly $\frac{1}{n+1}\binom{2n}{n}$ walks that return to $0$ and never have a negative partial sum.
And how do you get that? The immediate recursion "count number of paths that return at time $2k$ but no earlier and add up the result for $2n-2k$" looks a bit ugly.
After factoring the bottom, did you split up the fraction using partial fractions? Is the final step to integrate each fraction - giving Ln of each denominator?
@KannappanSampath may I ask about the problem I told you about yesterday? You became unresponsive after I posted it. Was it because it didn't interest you or for some other reason?
At the risk of being called an elitist, I for one would like to see some more candidates with a decent knowledge of mathematics. The current moderators are way above the threshold I would set for that but some of the current candidates so fare are struggling with the most basic things.
What Kannappan said. I don't believe mods have to be cutting-edge researchers, but they should have some amount of experience "herding cats", if you catch my drift...
@Gigili I didn't say anything of the kind. I don't think there's one single person that understands every question, after all. We only have two "professional mathematicians" currently (whatever that means) but there are quite a few tasks that a layman simply cannot perform: how to decide if an answer actually contributes something to the thread, for example?
@KannappanSampath I'm sorry if it appears curt. I was just thanking you for the explanation. I simply hadn't understood your unresponsiveness before. Now I do. :)
@KannappanSampath Oh, that's the other requirement for being a mod, at least in my book: somebody with a good understanding of "don't be a dick", and can apply it properly.
Ack, I saw that an edit was by "anon" and the original post was by "anon" so I accepted the edit which I thought would be better as a comment because I thought they were the same anon. I guess I will just roll it back.
@KannappanSampath I have a set [1, 2, 3, 4, 6, 9, 13, 19, 28, 41] and I am trying to figure out how many subsets fit condition X where X = largest element of subset is smaller than the sum of the rest of the subset
well it's from a PE problem and they're asking about a list 10^18 elements long... so I don't think it's an algorithm question because there's no way to iterate that high
I tried listing everything out by subset sizes to see if there was a pattern in how they grow from one n to the next but nothing seems to hold consistently
@JohnSmith That little bit, you should have mentioned in the question. :) If not from me, it's the first suggestion you'll receive on questions like that.
@Kanna: Well, he seems to be professing opinions irrelevant to actual moderator issues IMO. He's basically against the community downvoting things without explanation, or with too little charity, because it discourages newbies from using the site.
@leo: Surely you can figure out what $\limsup\limits_{x\to\infty}f(x)$ is from the information in that article?
Help, trying to find a list of the tex code that is allowed to used to post a question. The reason for this is because I tried \begin{array} but that didn't render. I have tried searching on se.tex and on there, but can't find it.
arrays should work in questions. anything that previews correctly is allowed, and then maybe a tiny bit more (because of potential bugs in the previewer)
It's possible you didn't correctly write the markup for your array, or your browser decided to take a nap. In the latter case refreshing should work, though be sure to copy everything you've written in case it wasn't all saved..
@anon thanks, but do you know if there is a check list I could review before trying to figure out how to write my question in (la)tex. I would be nice for a newbie of LaTeX to know what I can use, or what tags I should learn, so I can post a better question.
@anon Not to complain, but I have tried that and my code works on mike tex editor I have that runs under virtual box, it could be because I use chrome and the school I am at blocks or hampers the usages of non-Chinese websites.
Just because something works in miktex or a document creator does not mean it works on the mainsite (math.stackexchange). I'm talking about the preview that exists under the box where you type in your question; it's live.
@ymar I would doubt that anyone would care if you edited their post (a little) so that you could change a downvote to an upvote. However, I think you can change a downvote at any time; at least, I think I've had people rescind their downvote without my post being edited.
I rarely downvote, unless the question is really worth it, most of the time, I put a comment saying how they need to fix their question, or post an answer with sarcasm.
@MaoYiyi I thought that answer was completely trivial and I didn't even bother to comment on my downvote. It must have been unpleasant to the answerer. It's even more embarrassing because it's the only answer "competing" with mine in that question.
@MaoYiyi I have never downvoted. I would rather give a helpful comment. I haven't run into a case where the OP doesn't repair the error. If they didn't, I might downvote.
@ymar I see no reason not to upvote another's answer to a question you've answered (as long as the answer is good). It doesn't hurt the number of votes you get.
I don't like to downvote, mostly because I got so harshly downvoted asking about a book and all I could remember was that it had KY birds in it, then finally someone gave me the answer, but it really hurt. I understand now that my question was not worded as carefully as I could have worded it, but still, it wasn't a terrible question.
For sure, upvote when their answer is better than yours, or more complete. I like when people write nice answers, it helps me to write better English here.
Do you think I would be downvoted if I posted a questions in poor English, and then wrote what I wanted to say in another language? Mostly because I don't have the English skills to explain the question very well.
@ymar it was my first question and I got so downvoted, that I couldn't do anything, I finally send a message to some of the users that left comments and explained that I was searching for a book not being a pervert, and told them the title of the book.. Then one of the mods, fixed it and have me some points back and now I am very careful about what questions I ask.
this is utterly ridiculous. i've gone through like 30 OEIS sequences which all match like 12 terms of all these different ways of splitting up the problem and they ALL DIVERGE after a certain point
@robjohn Do you have a slight error in this comment? I get that $x^5+1=0$ factors to $x=e^{i(\frac{\pi}{5}+\frac{2k\pi}{5})} \quad (k \in \mathbb{Z})$. That means $x=e^{\frac{\pi}{5}},\ e^{\frac{3\pi}{5}},\ e^{\frac{5\pi}{5}},\ e^{\frac{7\pi}{5}},\ e^{\frac{9\pi}{5}}$
...but your equation seems to show $x=e^{0\frac{\pi}{5}},\ e^{\frac{2\pi}{5}},\ e^{\frac{4\pi}{5}},\ e^{\frac{6\pi}{5}},\ e^{\frac{8\pi}{5}}$
I'd say award to the answer you have got and leave a note saying although this answer does not answer the question, you wanted the bounty to be awarded in a useful way!
