Timeline for A conjecture on planar graphs
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2022 at 17:21 | history | edited | Michael Hardy | CC BY-SA 4.0 |
proper use of \deg
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| Jul 8, 2017 at 13:44 | comment | added | Peter Heinig | The "something more complicated" is the unique real solution of an equation $f(x)=0$ where $f$ in the relevant interval is a strictly monotone increasing Elementary function in the technical sense. This is perhaps getting too terminological, but: evaluating the average of the average of your function involves something like a function elementary relative to a non-algebraic equation. | |
| Jul 8, 2017 at 13:36 | comment | added | Peter Heinig | Just to summarize a bit, and to draw attention to the interesting concept of averages of higher order: it seems that the average of the average of your function (the number defined above) can more or less routinely be calculated to a precision you perhaps did not expect. For example, it seems that said second-order-average can be expressed "in terms" of elementary functions, and hence numerical approximation can be calculated to very many digits of accuracy. (But: something more complicated than "elementary functions" in the contemporary technical sense is involved.) | |
| Jul 5, 2017 at 11:36 | answer | added | monkeymaths | timeline score: 10 | |
| Jul 5, 2017 at 6:14 | vote | accept | Zur Luria | ||
| Jul 4, 2017 at 22:16 | answer | added | Brendan McKay | timeline score: 43 | |
| Jul 4, 2017 at 19:34 | history | edited | Turbo | CC BY-SA 3.0 |
deleted 16 characters in body
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| Jul 4, 2017 at 19:32 | comment | added | Peter Heinig | Conjecture (modulo details that I do not have time to write out): if $\mathrm{L}(G)$ denotes your function, and if $\mathcal{P}_n:= \text{set of all labelled planar graphs with n vertices}$, then $\frac{1}{\lvert\mathcal{P}_n\rvert}\sum_{G\in\mathcal{P}_n}\frac{\mathrm{L}(G)}{\lvert E(G)\rvert} \sim_{n\to\infty} 4.42652 + o(1)$. | |
| Jul 4, 2017 at 18:26 | comment | added | Peter Heinig | Just in the unlikely case that you are not aware of it and that in your work you need to know more about degree-distributions of planar graphs: it might be useful to have a look at the recent work of Drmota, Gimenez, and Noy. For example: arXiv:0911.4331v1 | |
| Jul 4, 2017 at 17:41 | history | edited | Zur Luria | CC BY-SA 3.0 |
added 61 characters in body
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| Jul 4, 2017 at 17:27 | history | asked | Zur Luria | CC BY-SA 3.0 |