Talk:Stirling numbers of the first kind

message: I know what it means. It's a common way to denote generating functions.
When writing out H(z,u) as an expansion in z, then [z^n]H(z,-1) is
the coeffient of the term with z^n with fixed u=-1. Likewise, [u^k]H(z,u)
is the coefficient of u^k when expanding H(z,u) in u. Imho, removing something
when you DON'T understand it is not correct (at most arrogant :p). It's
better to only remove things when you are an expert on the subject. Carlo Wood 06:13, 14 February 2007 (UTC)
replies: text: Yes, well, the conversation might be more productive if the actual issues  were addressed; being rude and insulting is not helpful. I'm not asking for much, I'm just asking for a definition of the terminology; this is common and accepted practice not just in WP but all academic writing, and is certainly spelled out in WP style guides. Not much point to an article if only the experts understand what it says.  linas 04:28, 19 March 2007 (UTC)

text: Dear Linas, I am definitely not angry, as you say on my talk page, since you are working very hard to make Wikipedia the best it can be. As for the article on Stirling numbers and EGFs, this is what I wrote in December 2006: "... the page also includes a link to Analytic combinatorics - Symbolic combinatorics., written by two of the most brilliant people in the field. May I respectfully suggest you have a look at it. You might find it exciting reading. As for the Stirling number/Generating function stuff, I agree it should not go into the main article, but we do not want to miss out on the powerful combinatorics techniques formalized in the eighties." So you see, this has nothing to do with me, or with proving anything. I simply believe that these developments from the eighties, which most specialists would agree count among the most significant in the field, should definitely find a place in Wikipedia. This "claim" is easy to verify. Just ask anyone in the math dept. of a university near you. Now, on the writing itself, which you say is flawed. Well, I couldn't agree more, as far as my contribution is concerned. I am not good at expository writing. But that's what the Wikipedia edit model is for, right? I hope you or someone else who is interested and qualified will make the necessary corrections and turn the article into a resource that is useful for everyone. (BTW the coefficient extraction operator has been documented on the formal power series page for some time now.) -Zahlentheorie 13:56, 19 March 2007 (UTC)
replies: text: As a professional combinatorialist who knows something about the subject, I believe most experts don't agree that these specialized developments "count among the most significant in the field", although they would not discount them either.  There is an article on Symbolic combinatorics according to Flajolet-Sedgewick, and their highly technical, not widely known, and usually unnecessary notation should be confined to that article.  Zaslav (talk) 20:08, 18 November 2012 (UTC)
thread_title:  Generating function 

message: Using the formulae provided, I was unable to reproduce the table provided on the page itself. It later turned out that in several places negative signs were missing ...
For example
:\left[{n+1\atop k}\right] = n \left[{n\atop k}\right] + \left[{n\atop k-1}\right]
should be 
:\left[{n+1\atop k}\right] = \left[{n\atop k-1}\right] - n \left[{n\atop k}\right]
Also
:\left[{n\atop n-1}\right] = {n \choose 2} 
should be
:\left[{n\atop n-1}\right] = -1 {n \choose 2},
And
:\left[{n\atop n-3}\right] = {n \choose 2} {n \choose 4}.
should be
:\left[{n\atop n-3}\right] = -1 {n \choose 2} {n \choose 4}.  —Preceding unsigned comment added by 217.34.163.161 (talk) 10:57, 22 July 2008 (UTC)
replies: text: The formulae in the article are correct, since \left[{n\atop k}\right] is the unsigned Stirling number. /Pontus (talk) 10:44, 22 August 2008 (UTC)
thread_title: Inaccurate!!

message: This section is quite unclear, badly formated, and not sourced. Are you sure it is needed ? Compare with the French version :fr: Nombre_de_Stirling#Formules_explicites for more interesting formulas... --Dfeldmann (talk) 06:15, 2 March 2010 (UTC)
replies: text: Because the formula is more complicated than standard one and seems not to be reviewed, I don't think it is important. See also Talk:Stirling number#explicit formula and Talk:Stirling number#crazy formula. The IP user added this kind of formula to French Wikipedia, Japanese Wikipedia (my home wiki), etc. Some of these are already removed. --白駒 (talk) 22:02, 18 March 2010 (UTC)
thread_title:  Explicit formula 

message: I believe (from experience) that the most common notation for Stirling numbers of the first kind nowadays is s(n,k).  The notation with brackets seems to be relatively rare.  It also conflicts with the notation for Gaussian coefficients.  Hence, I suggest changing the notation in this article.  Is there a reason not to do so?  
It is also a good idea to get rid of the "symbolic combinatorics" notations that contribute mostly confusion.  The article on "symbolic combinatorics", which is not a widespread method but only one theory of combinatorial enumeration, is the right place for these notations.  Zaslav (talk) 20:15, 18 November 2012 (UTC)
replies: text: Sounds fine to me.  Stanley and Bona both use c(n, k) for the unsigned numbers (I guess c for "cycle"?).  By the way, I was looking it over and thinking that the "explicit formula" section seems like a lot of space for a pretty marginal formula; what do you think? --JBL (talk) 20:56, 18 November 2012 (UTC)
replies: text: The "explicit formula" is an important one but the way it was written is uselessly complicated.  I've simplified it but I'm not sure it's correct.  I will look into that later, unless someone beats me to it. Zaslav (talk)
* Bracket notation is used in Concrete Mathematics and gaining popularity since then. Maxal (talk) 04:49, 19 November 2012 (UTC)

text: I don't think bracket notation has become very common.  Disadvantages: it is space-consuming, and conflicts with common notation for Gaussian coefficients.  I'm disinclined to keep it.  But let's keep the discussion going for a while.  Zaslav (talk) 03:33, 20 November 2012 (UTC)
replies: text: Since bracket notation has not gained predominance and, worse, is in outright conflict with the standard bracket notation for Gaussian coefficients, and since there has been no further comment objecting, I will change the notation to s(n,k), which I believe to be more prevalent than other notations these days (based on admittedly limited reading), with the comment that there are other notations.  If anyone has a comment about this, please write it here, and thanks. Zaslav (talk) 02:51, 15 November 2013 (UTC)
thread_title:  Notation for Stirling numbers