Talk:Gaussian binomial coefficient

Notation
I have two comments about this page to put up for discussion:
 * First, it seems to me that "Gaussian binomial" is the least used of the many names for these objects. I nominate "Gaussian coefficients."
 * Second, instead of
 * $${m\choose r}_q,$$

I am more used to seeing
 * $$\begin{bmatrix}n\\k\end{bmatrix}_q.$$

Would there be any objections to making these changes?


 * Well, the reason for both the name and the notation, is to parallel binomial coefficient. The new square braket notation will remove this analogy, which is probably not good. Oleg Alexandrov 17:52, 15 Apr 2005 (UTC)


 * I agree that the parallel to binomial coefficients would be nice, if that were indeed the way people wrote these things. It's just that that's not how I've seen it done. Vince Vatter 18:13, 15 Apr 2005 (UTC)


 * You would need to contact the main author of this then --> Linas. Cheers, Oleg Alexandrov 18:17, 15 Apr 2005 (UTC)

In addition to the above notations, I have also seen just plain old
 * $$\begin{bmatrix}n\\k\end{bmatrix}$$

(without the subscript q), and also a version of
 * $${m\choose r}$$

where all the symbols (including the outer parentheses) are in bold. (The latter is what Stanley uses in Enumerative Combinatorics). I don't know how to get bolded parentheses in latex (let alone texvc). I think all are acceptable; I don't know which is the most common. Dmharvey Talk 1 July 2005 13:20 (UTC)


 * The version with square brackets seems inferior to me, in particular when also dropping the q (and what if one wants another indeterminate?), notably in view of the notation for the unsigned Stirling numbers of the first kind with which it conflicts (don't know right now whether those have a universally accepted q-analog, but one had better not get in the way in case some day they do). Actually I don't see any reason to use square brackets that nobody uses for binomial coefficients,it certainly does not stress the analogy. Marc van Leeuwen (talk) 09:04, 25 March 2010 (UTC)

Some arguments in favor of the q-notation can be found in Knuth's paper Two notes on notation, arxiv:math/9205211v1, together with some historical background and overview. 141.2.26.29 (talk) 14:41, 4 August 2010 (UTC)

conventions for out-of-range inputs?
What are the conventions for the definition of
 * $${m \choose r}_q$$

when r < 0 or r > m? Is it then zero, similarly to the ordinary binomial coefficient situation? Dmharvey Talk 1 July 2005 13:24 (UTC)

Move to Gaussian binomial coefficient
I agree entirely with the above comment that the name of this article is not appropriate. A quick Google scholar search tell me that "Gaussian binomial" is alwas followed by "coefficient". Indeed it is absurd to call this a binomial, since it almost never has two terms. Since in five years time nobody really contested the criticism, I will move this article to "Gaussian binomial coefficient", and adapt the text accordingly. Of course "Gaussian coefficient" and "q-binomial coefficient" are also often found. Ironically, the main problem with Gaussian coefficients seems to be that there is no obvious q-binomial theorem in which they appear as coefficients. There is such a formula form their "multiset number" analogs
 * $$\left(\!\!\binom nk\!\!\right)_q=\binom{n+k-1}k_q,$$

namely
 * $$\sum_{k\in\N}\left(\!\!\binom nk\!\!\right)_qX^k=\prod_{0\leq i<n}\frac1{1-q^iX}.$$

Since to my surprise I have not found this formula stated anywhere clearly, I'll leave it out of the article as per WP:NOR, but surely a more decent search should easily locate this fact somewhere. Marc van Leeuwen (talk) 08:58, 25 March 2010 (UTC)

Oops, I admit to not reading this article carefully, the formula is there. Marc van Leeuwen (talk) 09:28, 25 March 2010 (UTC)

Source for the name?
I have been unable to find a source for the name "Gaussian" for these coefficients. (I admit to not having looked very far.) It would be good to include this somewhere. —Preceding unsigned comment added by 129.89.14.247 (talk) 15:51, 14 June 2010 (UTC)

You can get many references by searching for "Gaussian coefficients", like this reference. Or you can go for "Gaussian binomial coefficients" like this book. Marc van Leeuwen (talk) 15:24, 16 June 2010 (UTC)

Best name for article
In reading I've often seen "Gaussian coefficient", also "q-binomial" and "q-Gaussian", and never "Gaussian binomial coefficient". The title of the article should be "q-Binomial coefficient", as the most commonly used name, or "Gaussian coeffieient" as the runner up. I bring this question up for consideration.

I say most common based on a survey of MathSciNet reviews from 2000-1015. I found 9 reviews that contain "Gaussian binomial coefficient", 16 that contain "Gaussian coefficient" (after excluding about 18 where "Gaussian coefficient" means a random variable with Gaussian distribution) or "q-Gaussian coefficient", > 100 "q-binomial", a few "Gaussian q-binomial". Fairly often, two names are mentioned; this shows me that no one name is dominant. Zaslav (talk) 02:29, 17 August 2015 (UTC)


 * I agree. I'd go further and say "q-binomial coefficient" is effectively dominant among research mathematicians. Stanley's EC1 also uses it as the primary name, which counts for a lot in my book. Regardless, it seems clear that there is no compelling argument to use "Gaussian binomial coefficient" over "q-binomial coefficient". As far as I can tell, this was named "Gaussian binomial coefficient" when it was just a stub and that sub-par name has stuck around for years. 50.132.4.93 (talk) 06:40, 4 December 2015 (UTC)


 * Yes, move to q-binomial coefficient as the proper name, per above. 67.198.37.16 (talk) 22:35, 5 January 2024 (UTC)