Timeline for Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = b_n$? [closed]
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2017 at 14:31 | history | closed |
Ben McKay Henry.L R.P. Stefan Waldmann Mikhail Katz |
Needs details or clarity | |
| Sep 6, 2017 at 19:34 | review | Close votes | |||
| Sep 7, 2017 at 14:32 | |||||
| Apr 12, 2010 at 2:58 | history | edited | mingming | CC BY-SA 2.5 |
added 2 characters in body; edited title
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| Apr 12, 2010 at 2:47 | history | edited | mingming | CC BY-SA 2.5 |
added 355 characters in body
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| Apr 12, 2010 at 1:22 | comment | added | Qiaochu Yuan | mingming, I hope you can see that this is not the question you originally asked. | |
| Apr 12, 2010 at 1:19 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Apr 12, 2010 at 1:07 | comment | added | mingming | Dear Tom: When I write a to be a_{n} then there is a reciprocity between alpha_{k} and a_{n}. I just want more information about this equation. | |
| Apr 12, 2010 at 0:55 | comment | added | Tom Leinster | (But I don't see any more sense in it than darij and Qiaochu. Maybe the questioner can clarify his/her meaning.) | |
| Apr 12, 2010 at 0:54 | comment | added | Tom Leinster | Well, I've edited it now to reflect the questioner's apparent meaning. To those reading this later: the original version used curly brackets around the n and k. | |
| Apr 12, 2010 at 0:52 | comment | added | Qiaochu Yuan | I read the problem as a sum from k = 0 to n and I read the brackets as binomial coefficients, so {n choose 0} = 1. Also, {n choose n} = 1. Either way, all but one of the alpha_i uniquely determines the last one, which is always an integer. | |
| Apr 12, 2010 at 0:52 | history | edited | Tom Leinster | CC BY-SA 2.5 |
clarified meaning and smartened up Latex; edited title
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| Apr 12, 2010 at 0:50 | comment | added | Tom Leinster | Ah, so it's a notation problem. Mingming, {n, k} is often used to mean the number of partitions of an n-element set into k classes; so then {n, 1} = 1. Use round brackets for binomial coefficients. | |
| Apr 12, 2010 at 0:44 | comment | added | mingming | {n, k} is the binormal coefficient which is n choose k. {n, 1} is n. | |
| Apr 12, 2010 at 0:38 | comment | added | Qiaochu Yuan | darij has already told you what the general solution is. I really don't think you are asking the question you mean to ask. | |
| Apr 12, 2010 at 0:03 | comment | added | mingming | Can you write down a general solution to this Diophantine Equation? | |
| Apr 11, 2010 at 23:49 | comment | added | Qiaochu Yuan | Yes, so you can choose values of the other alpha_k, k > 0 arbitrarily and this determines the value of alpha_0 (which I'm sure is what darij meant to say). Perhaps you meant to ask about a sequence a_n on the right? | |
| Apr 11, 2010 at 23:40 | comment | added | mingming | a is a fixed integer and this is an equation about alpha_{k}? | |
| Apr 11, 2010 at 23:36 | comment | added | darij grinberg | What exactly do you want? {n, 1} is 1, so alpha_1 is always uniquely determined by the other alpha_i. | |
| Apr 11, 2010 at 23:33 | history | asked | mingming | CC BY-SA 2.5 |