Timeline for Prove positivity of rational functions
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 12, 2022 at 19:08 | comment | added | Max Alekseyev | @FedorPetrov: Essentially this argument equivalent to the use of Vandermonde's identity: $$\binom{n+r-2}{r-2} = \sum_{k=1}^{r-1} \binom{n-1}{k-1}\binom{r-1}{r-1-k}$$ and noticing that $\binom{r-1}{r-1-k}\geq 1$. With a bit of extra effort I got a bit stronger bound. | |
| May 12, 2022 at 18:52 | comment | added | Fedor Petrov | $\binom{n+r-2}{r-2} - \sum_{k=1}^{r-1} \binom{n-1}{k-1}$ is non-negative also by a simple combinatorial reasons: take $n-1$ boys and $r-1$ girls and choose $r-2$ children from them: if you fix the chosen $k-1$ boys, you may always add $r-k-1$ girls to them. | |
| May 12, 2022 at 18:32 | vote | accept | T. Amdeberhan | ||
| May 12, 2022 at 17:44 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| May 12, 2022 at 17:34 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
added 4 characters in body
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| May 12, 2022 at 17:25 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
added 148 characters in body
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| May 12, 2022 at 17:10 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
a bit better; added 3 characters in body; edited body
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| May 11, 2022 at 11:34 | history | answered | Max Alekseyev | CC BY-SA 4.0 |