Timeline for How to interpret this result modulo $(y-1)^{n+1}$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2023 at 19:15 | answer | added | Peter Taylor | timeline score: 1 | |
| May 4, 2023 at 12:07 | comment | added | Oleksandr Kulkov | Oh I see, thanks for noting! I'm still not sure about the exact interpretation in the given context though... | |
| May 4, 2023 at 12:04 | comment | added | Martin Rubey | What I meant to say is that in this form you can interpret it combinatorially, because the coefficients are (essentially) positive and meaningful. | |
| May 4, 2023 at 12:00 | comment | added | Oleksandr Kulkov | To the best of my knowledge, the exact value of the LHS is $$\frac{1}{1-xy} \left(y^{n+1} - \left(\frac{y-1}{1-x}\right)^{n+1}\right).$$ You can get it by expanding $$D^{n+1} uv = \sum\limits_{k=1}^{n+1} \binom{n+1}{n} D^{n-k} u D^{k+1} v,$$ but still it's a low-lever symbolic manipulation rather than high-level explanation/interpretation... | |
| May 4, 2023 at 11:53 | comment | added | Martin Rubey | If I'm not mistaken, the difference of the two sides is $(y-1)^{n+1} \sum_{m, k} \binom{k+n}{n} y^{m-k} x^m$, which looks quite doable. | |
| May 4, 2023 at 10:49 | history | asked | Oleksandr Kulkov | CC BY-SA 4.0 |