Timeline for (Conceptual) proof and/or interpretation of a $q$-binomial identity
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2022 at 10:01 | answer | added | Fedor Petrov | timeline score: 5 | |
| Dec 15, 2022 at 9:52 | comment | added | Vladimir Dotsenko | @Z.M Ah, I see - you suggest to expand each $q^\alpha$ around $q=1$. Yes, that is a perfectly valid point, thanks! | |
| Dec 15, 2022 at 9:47 | comment | added | Z. M | Hopefully I am not too mistaken. The $q$-binomial coefficient $\binom\alpha k_q$ makes sense for formal variables $\alpha$, and is defined in a similar fashion to the usual one: $\binom\alpha k_q=[\alpha][\alpha-1]\cdots[\alpha-k+1]/[k]!$ where $[\alpha]=(1-q^\alpha)/(1-q)\in\mathbb Z[\alpha][\![q-1]\!]$. | |
| Dec 15, 2022 at 9:30 | vote | accept | Vladimir Dotsenko | ||
| Dec 15, 2022 at 9:26 | answer | added | Neil Strickland | timeline score: 6 | |
| Dec 15, 2022 at 9:19 | comment | added | Vladimir Dotsenko | @Z.M can you elaborate? I mean, these are not quite polynomials in $a,b$ as written. | |
| Dec 15, 2022 at 9:15 | comment | added | Z. M | I would expect that this identity is true without assuming that $a,b$ are integers, namely, it is an identity in $\mathbb Z[a,b][\![q-1]\!]$. | |
| Dec 15, 2022 at 9:03 | history | asked | Vladimir Dotsenko | CC BY-SA 4.0 |