Timeline for Partial sums of the Chu--Vandermonde identity
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2020 at 15:19 | comment | added | Student | OP asked for a lower bound for the partial sum, and it's never answered directly. I don't have an answer either, but realize that it might be helpful to look into Hypergeometric Distribution. In particular, an upper bound of the tail is given in the link. However, no lower bound yet has been given. One has to turn to finer analysis of hypergeometric distributions. Hopefully someone can make this answer complete. ((also related: mathoverflow.net/questions/357560/…)). | |
| Jun 28, 2015 at 9:11 | comment | added | Sergei | The AGM inequality gives some trivial lower bound, not so? | |
| Jul 27, 2010 at 14:28 | vote | accept | Carla | ||
| Jul 26, 2010 at 13:34 | comment | added | JBL | The problem (essentially) asks for the probability that, when $k$ balls are selected at random from among $n + m$, at most $d$ of those selected come from the first $n$. | |
| Jul 26, 2010 at 12:38 | comment | added | Wadim Zudilin | @JBL: I would be happy to agree with you but I am not convinced that some part of a natural binomial sum is "interesting". Unless the author gives some combinatorial background for it. For the moment, there is no combinatorics in the OP. | |
| Jul 26, 2010 at 11:30 | comment | added | JBL | Wadim, computing asymptotics of "interesting" combinatorial expressions is surely part of combinatorics! | |
| Jul 26, 2010 at 10:58 | history | edited | Wadim Zudilin | CC BY-SA 2.5 |
slightly edited and retagged
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| Jul 26, 2010 at 10:52 | answer | added | Wadim Zudilin | timeline score: 6 | |
| Jul 26, 2010 at 9:35 | comment | added | Pietro Majer | I'm not sure I understand: what's the "relaton between $d$ and $k$": do you mean the ratio $d/k$ ? (Fixed typo in the title) | |
| Jul 26, 2010 at 9:34 | history | edited | Pietro Majer | CC BY-SA 2.5 |
deleted 2 characters in body; edited title
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| Jul 26, 2010 at 9:16 | comment | added | Wadim Zudilin | Your problem is not from "combinatorics": you ask for analytic (asymptotic) estimates for binomial coefficients. There is a book by de Brijn, "Asymptotic methods in analysis", which discuss this sort of problems; you may also have a look at mathoverflow.net/questions/27912. | |
| Jul 26, 2010 at 8:57 | history | asked | Carla | CC BY-SA 2.5 |