Timeline for The stabilizer of the conditionally convergent series
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 20, 2017 at 22:20 | comment | added | Gro-Tsen | There's a finer sufficient condition for being sum-preserving given in Bourbaki, TG (=Topologie Générale), IV, §7, exercise 12 (page IV.60 in the French edition), namely that $r(n) := |\sigma(n)-n|\cdot\sup_{m\geq n}|\alpha(m)|$ tends to $0$. I seem to remember there's a slight mistake and that it should be something different (maybe replace some $m$ or $n$ by $\sigma(m)$ or $\sigma(n)$), I guess solving the exercise will unravel the correct version. | |
| Jun 20, 2017 at 21:18 | comment | added | Johannes Hahn | Maybe I'm blind, but why are G and H even groups? | |
| Jun 20, 2017 at 21:08 | history | edited | Michael Hardy | CC BY-SA 3.0 |
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| Mar 6, 2017 at 4:04 | vote | accept | Jeff Strom | ||
| Mar 5, 2017 at 19:24 | answer | added | Zach Teitler | timeline score: 3 | |
| Mar 1, 2017 at 5:15 | comment | added | Zach Teitler | If there is a constant $C$ such that $|\sigma(n)-n| \leq C$ for all $n$, then $\sigma$ is sum-preserving. And this "boundedness" property is preserved by compositions and inverses. So one might guess that perhaps these are all of the sum-preserving permutations. But it is not the case. There are sum-preserving permutations that have "unbounded steps" (but, I suppose, very far apart). There are several known characterizations of sum-preserving permutations, see for example projecteuclid.org/euclid.pjm/1102688295 and references therein. | |
| Mar 1, 2017 at 4:13 | history | edited | Jeff Strom | CC BY-SA 3.0 |
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| Mar 1, 2017 at 2:53 | history | asked | Jeff Strom | CC BY-SA 3.0 |