Timeline for How large can the dimension of a 'Span of powers of a finite field basis' be?
Current License: CC BY-SA 4.0
39 events
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| Dec 12 at 21:09 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 14 at 21:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Dec 18, 2023 at 19:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 20, 2023 at 19:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 22, 2023 at 18:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 23, 2022 at 18:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 25, 2022 at 19:01 | comment | added | LSpice | Are you still planning to add that answer? | |
| Aug 25, 2022 at 18:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 27, 2022 at 17:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 28, 2021 at 17:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 30, 2021 at 16:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 1, 2021 at 2:31 | comment | added | actcon | I proved $M_{p^k}^{(d)} \ge \text{ord}_t(p)$, where $t=\frac{p^k-1}{\gcd(p^k-1,d)}$. I am already very satisfied with this fact. I will add an answer to the post after weekends. Thank you all for discussions:) | |
| Jul 31, 2021 at 16:18 | comment | added | მამუკა ჯიბლაძე | What might be true is that if $\beta_1$, ..., $\beta_{ij}$ is a basis of $\mathbb F_{p^{ij}}$ then $\beta_1^d$, ..., $\beta_{ij}^d$ span $\mathbb F_{p^j}$ for $d=\frac{p^{ij}-1}{p^j-1}$ | |
| Jul 31, 2021 at 16:13 | comment | added | მამუკა ჯიბლაძე | You are right, I should be more careful. I only could write "$\leqslant j$", not "$=j$". Presumably there are also examples of "$<j$" for $i>1$... | |
| Jul 31, 2021 at 15:59 | comment | added | actcon | @მამუკაჯიბლაძე: In your last comment, what does $i$ denote? If I am free to choose $i=1$, then it contradicts the experiments with $M_{p^k}^{(d)}\neq k$. | |
| Jul 31, 2021 at 15:50 | history | edited | actcon | CC BY-SA 4.0 |
moved a conjecture to a fact
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| Jul 31, 2021 at 14:01 | comment | added | მამუკა ჯიბლაძე | (...which is more or less obvious: $\beta^{\frac{p^{ij}-1}{p^j-1}}\in\mathbb F_{p^j}$ for any $\beta\in\mathbb F_{p^{ij}}$) | |
| Jul 31, 2021 at 13:47 | comment | added | მამუკა ჯიბლაძე | More generally, $M_{p^{ij}}^{\left(m\frac{p^{ij}-1}{p^j-1}\right)}=j$ | |
| Jul 31, 2021 at 13:37 | comment | added | actcon | I updated the experimental results for p=3,5. Sorry, my code contained an error. | |
| Jul 31, 2021 at 13:35 | history | edited | actcon | CC BY-SA 4.0 |
fixed experimental results for p=3 and p=5
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| Jul 31, 2021 at 12:11 | comment | added | მამუკა ჯიბლაძე | It seems that $M_{p^k}^{\left(m\frac{p^k-1}{p-1}\right)}=1$ for all $p$, $k$ and $m$ | |
| Jul 31, 2021 at 8:28 | history | edited | actcon | CC BY-SA 4.0 |
added a conjecture
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| Jul 31, 2021 at 8:19 | history | edited | actcon | CC BY-SA 4.0 |
typo
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| Jul 31, 2021 at 7:14 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jul 31, 2021 at 7:12 | history | edited | actcon | CC BY-SA 4.0 |
typo
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| Jul 31, 2021 at 7:01 | history | edited | actcon | CC BY-SA 4.0 |
added experimental results
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| Jul 31, 2021 at 6:46 | comment | added | actcon | @MarkSapir: $M^{(d)}_8 = 3$ holds for $d=3,5,6$. However, $M^{(7)}_8 = 1$. I will add some experimental results to the question soon. | |
| Jul 31, 2021 at 6:31 | comment | added | markvs | Then what is it for $\mathbb{F}_8$. Is it $3$. and, in general, $k$ for every odd $k$? | |
| Jul 31, 2021 at 5:12 | answer | added | Donggeon Yhee | timeline score: 0 | |
| Jul 31, 2021 at 4:25 | history | edited | actcon | CC BY-SA 4.0 |
corrected "k" to "k-1" in the second bullet-item
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| Jul 31, 2021 at 4:24 | comment | added | actcon | Oops, my bad... I meant $d \ge 3$ | |
| Jul 31, 2021 at 4:09 | comment | added | markvs | ok. So we can assume that $d>3$, $d\ne 4=2^2$ and $p=2$. What is it for $\mathbb{F}_{32}$? | |
| S Jul 31, 2021 at 3:48 | history | suggested | markvs | CC BY-SA 4.0 |
Fixed misprint in the title
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| Jul 31, 2021 at 3:46 | comment | added | actcon | @MarkSapir: For the special case of d=2, I am interested in the p>2 case, since the p=2 case is trivial by the first bullet-item. For the general case of d>3, I am more interested in the p=2 case. Thank you for your attention:) | |
| Jul 31, 2021 at 3:37 | review | Suggested edits | |||
| S Jul 31, 2021 at 3:48 | |||||
| Jul 31, 2021 at 3:34 | comment | added | markvs | $p\ne 2$? ${}{}{}{}$ | |
| Jul 31, 2021 at 2:16 | review | First posts | |||
| Jul 31, 2021 at 6:18 | |||||
| Jul 31, 2021 at 2:13 | history | asked | actcon | CC BY-SA 4.0 |