Timeline for The critical exponent function
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2020 at 21:35 | comment | added | Alessandro Della Corte | It is (I assume you rather meant that, in your hypothesis, $\kappa_{2^n}(x)\to 1$). And no, it isn't obvious to me that you can't have a binary sequence whose "limsup" critical exponent is 1. | |
| Dec 11, 2020 at 3:37 | comment | added | Ronnie Pavlov | I was thinking of $\limsup_{\ell \rightarrow \infty} (\sup\{\alpha : \textrm{ there exists a word $w$ of length $\ell$ whose $\alpha$-power appears as a factor}\})$, but I think that this is probably equivalent to yours. | |
| Dec 8, 2020 at 21:51 | comment | added | Alessandro Della Corte | Do you mean $\limsup_{\ell\to\infty}(\sup \{\alpha:\, \text{there is a factor of length $\ell$ which appears as an $\alpha$-power}\})$? | |
| Dec 8, 2020 at 18:26 | history | answered | Ronnie Pavlov | CC BY-SA 4.0 |