Timeline for Values of the determinants $\det[(j-k)^m+\delta_{jk}]_{1\le j,k\le n}\ (m=1,2,3,\ldots)$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2022 at 18:37 | history | edited | or43 | CC BY-SA 4.0 |
Formula now valid for all $m$ and $n$, also cleaned up proof and addressed the general case explicitly
|
| Jul 1, 2022 at 11:41 | comment | added | Zhi-Wei Sun | It's a pity that some good solutions at MathOverflow will never appear in any formal paper. | |
| Jul 1, 2022 at 11:40 | comment | added | Zhi-Wei Sun | Of course, you can pose your solution at once. If you don't want to write any paper about this, we will not do so either since you are the main contributor to the answer. | |
| Jul 1, 2022 at 5:21 | comment | added | or43 | Thank you, it's kind of you to offer, but I would rather not put my name on anything. If you're writing a paper on this, I don't want to get in the way, and I can post my solution once you're done. | |
| Jul 1, 2022 at 3:34 | comment | added | Zhi-Wei Sun | Okay, you may pose your solution. Are you interesting in writing a joint paper with us concerning my questions here? | |
| Jul 1, 2022 at 2:15 | comment | added | or43 | Great! I believe I now also have a proof that the corresponding formula works for all $n$, for a general polynomial in $j, k$. I would like to post it here at some point, if it's alright with you. | |
| Jun 30, 2022 at 10:46 | comment | added | Zhi-Wei Sun | Joint with my student Han Wang, we have shown that the formula for $D_m(n)$ in the answer of or43 holds for all $m,n=1,2,3,\ldots$, and that for each positive integer $m$, $D_m(n)$ is indeed a polynomial in $n$ of degree $(m+1)^2$. | |
| Jun 29, 2022 at 12:24 | comment | added | Zhi-Wei Sun | I have checked your formula for $D_m(n)$. It is correct for all $m,n=1,\ldots,50$. Also, your formula supports my general conjecture. | |
| S Jun 29, 2022 at 9:34 | review | First answers | |||
| Jun 29, 2022 at 9:58 | |||||
| S Jun 29, 2022 at 9:34 | history | answered | or43 | CC BY-SA 4.0 |