Timeline for Sets of unit fractions with sum $\leq 1$
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2017 at 18:10 | history | edited | Mikhail Tikhomirov | CC BY-SA 3.0 |
post-mortem
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| Sep 14, 2017 at 18:02 | vote | accept | Mikhail Tikhomirov | ||
| Sep 14, 2017 at 17:37 | answer | added | RaphaelB4 | timeline score: 18 | |
| Sep 14, 2017 at 15:50 | answer | added | js21 | timeline score: 12 | |
| Sep 14, 2017 at 13:41 | comment | added | Jay Pantone | Differential approximation is a numerical estimation technique that uses known terms of a series to construct many linear differential equations with series expansions that match the known terms (and likely don't match later, unknown, terms). Then, the asymptotic behavior of the linear ODEs is read off and coalesced in a particular way, leading to an non-rigorous estimate of the asymptotic behavior of the sequence. It tends to be very accurate in practice. You can find more info (and more references) in the first 4 sections here: arXiv | |
| Sep 14, 2017 at 13:30 | comment | added | Mikhail Tikhomirov | Thank you Jay, this looks great! Can I ask you of a more in-depth explanation in an answer? | |
| Sep 14, 2017 at 13:25 | comment | added | Jay Pantone | Differential approximation suggests that the sequence grows like $C\alpha^nn^{\gamma}$ where $\alpha \in [1.8805,1.8807]$ and $\gamma \in [-0.498, -0.494]$. This would imply $\beta \in [0.9111, 0.9113]$. | |
| Sep 14, 2017 at 13:05 | answer | added | karpasi | timeline score: 6 | |
| Sep 14, 2017 at 12:32 | comment | added | Suvrit | Somehow it seems that a similar question was asked on MO many years ago, unfortunately I cannot find it right now. Perhaps someone else can! | |
| Sep 14, 2017 at 12:25 | history | edited | Mikhail Tikhomirov | CC BY-SA 3.0 |
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| Sep 14, 2017 at 12:19 | history | edited | Mikhail Tikhomirov | CC BY-SA 3.0 |
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| Sep 14, 2017 at 12:13 | history | edited | Mikhail Tikhomirov | CC BY-SA 3.0 |
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| Sep 14, 2017 at 12:06 | comment | added | Max Alekseyev | The data in the OEIS suggest that $\beta$ may be larger than 0.88 | |
| Sep 14, 2017 at 11:51 | comment | added | Max Alekseyev | oeis.org/A212657 | |
| Sep 14, 2017 at 11:49 | answer | added | Lucia | timeline score: 37 | |
| Sep 14, 2017 at 10:50 | history | edited | Venkataramana | CC BY-SA 3.0 |
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| Sep 14, 2017 at 10:22 | history | edited | Mikhail Tikhomirov | CC BY-SA 3.0 |
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| Sep 14, 2017 at 10:16 | history | asked | Mikhail Tikhomirov | CC BY-SA 3.0 |