Talk:Symbolic method (combinatorics)

Obscure and incomprehensible article

This article is an incomprehensible account of one specialized theory of combinatorial enumeration due to Flajolet et al. It is completely opaque to the uninitiated reader. I propose it be deleted or rewritten from the ground up.

I plan to merge into this article the so-called "Fundamental theorem of combinatorial enumeration" and let anyone who cares to do so take care of the rewriting. Zaslav (talk) 02:21, 28 May 2011 (UTC)

Merge done. Changed link "Fundamental theorem of combinatorial enumeration" due to merge. Zaslav (talk) 21:57, 25 December 2011 (UTC)

Classes (or species) are not easy to present. When vulgarizing, the material looks like some tricks that old grandpa shows us. When trying to build a rigorous language to write the classes (or species) equations, the material goes rapidly the other way, starting looking like a hard logical-semantical theory or extremely abstract algebra.

Asking initiated people their opinion on this stuff, I never heard the same answer

• nuclear math
• under-arithmetics
• combinatorial logic
• patterns
• containers
• cabal of egf-ology and so on.

The species belong to math like the synthetic geometry does. When Euclid says that line glide along itself, this stuff says : It is necessary to fix only one point to block all. The article is about very simple facts that are really hard to rigorously describe. The classes (or species) will always represent a linguistic challenge.Nicolae-boicu (talk) 19:56, 11 July 2012 (UTC)

Objections from former talk page of "Fundamental theorem of combinatorial enumeration"

The following is the talk page of "Fundamental theorem of combinatorial enumeration", moved here when that article was moved into "Symbolic combinatorics". Zaslav (talk) 21:19, 25 December 2011 (UTC)

Article is obscure and should be deleted

This article is an unintentional work of obfuscation. The name "fundamental theorem of combinatorial enumeration" is not standard and it could refer to any number of things. Google reveals very few uses of the phrase "fundamental theorem of combinatorial enumeration", and most of the hits that it does have are derived from Wikipedia itself. The phrase is pretentious. The theorem here is a cumbersome and highly formal generalization of some good ideas in combinatorics. It is an unworkable idea for enumerative combinatorics to have a "fundamental theorem"; it is like having a universal solvent in chemistry. While the theorem here has some merit, the entire article should simply be folded into the article on symbolic combinatorics. Greg Kuperberg (talk) 17:29, 26 May 2010 (UTC)

I agree with Kuperberg, except that I don't know whether or not the article merits merging into another article. All his objections are valid. There is no such thing in enumerative combinatorics as an acknowledged "fundamental theorem". I also found the article to be extraordinarily technical, overspecialized, and obscure. Zaslav (talk) 02:14, 28 May 2011 (UTC)

I disagree. The 'fundamental theorem' is taken from the context of Flajolet's work. For a better understanding: https://www.youtube.com/playlist?list=PLhsb6tmzSpiwyQCl4jmVPZymDs1MYIa8o — Preceding unsigned comment added by 2610:130:102:800:AD02:EB40:9F27:1113 (talk) 20:07, 14 March 2017 (UTC)

There is something to be said about making this article more understandable, for instance: "Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots. " Good luck — Preceding unsigned comment added by 2610:130:102:800:AD02:EB40:9F27:1113 (talk) 20:08, 14 March 2017 (UTC)

Merger proposal

{{mergefrom|Stirling numbers and exponential generating functions|discuss=Talk:Symbolic combinatorics#Merger proposal|date=December 2011}}

Wrong title

The article appears to be about "symbolic combinatorics", not analytic combinatorics in general. How did it get the new name? Zaslav (talk) 06:42, 24 January 2015 (UTC)

The title of Flajolet and Sedgewick's book is "Analytic Combinatorics". The name of their annual conference (now run primarily by Sedgewick) is "Analytic Algorithmics and Combinatorics (ANALCO)". Do you have a source for your assertion that they are using the wrong name for the thing that they do? If they call it "analytic combinatorics" and others call some other notable topic "analytic combinatorics", then the proper Wikipedia solution is to have two articles on the different subjects, with disambiguators in the title and with hatnotes or a disambiguation page, it is not to make up a new name for one of the two subjects or to change its article to be instead about the other one. —David Eppstein (talk) 07:40, 24 January 2015 (UTC)

May I remind you that the original title of this article was "Symbolic combinatorics" (follow the link). Also, in the article, e.g., "A theorem in the Flajolet–Sedgewick theory of symbolic combinatorics ...".

You misunderstood my point, which I agree was not made clear. I'm not "assert[ing] that they are using the wrong name for the thing that they do". I meant that "analytic combinatorics" is a field, not a theory. I found it objectionable, first, that this article, at least in its introduction, describes analytic combinatorics as if it's mainly due to Flajolet-Sedgwick, with previous contributions, and second, that it is not only about analytic methods in combinatorics; thus, I thought the previous name was at least as good (maybe not good either). There was plenty of analytic combinatorics before Flajolet-Sedgewick. I was skeptical that they had created the modern theory of analytic combinatorics.

As for their "symbolic combinatorics", which is included in this article, it appears to be a method of setting up generating functions. That is not analytic. Stanley, if one believes the title of his book, would call setting up generating functions enumerative. It could also reasonably be called algebraic. I believe this article would make more sense if the non-analytic part were separated out and presented as the Flajolet-Sedgewick method.

The fact that they call their book and conference Analytic Combinatorics is immaterial. There are many books (and conferences) that are more specialized or more generalized than what the title promises.

I have no time to follow this further; it's not a particular interest of mine; I don't want to fight; and it's hours past bedtime. Bye. Zaslav (talk) 10:29, 2 February 2015 (UTC)

The problem here is not that Flajolet and Sedgewick's field is not appropriately analytic. It's that the actual analytic methods are entirely left out of the article. This article describes what's referred to in the book(s) as the symbolic method, but has nothing at all to say about the analytic transfer theorem, which is where the half the name of the subject comes from.67.214.11.158 (talk) 04:59, 14 April 2016 (UTC)

What about this proposal?

• Write the article Analytic_combinatorics focusing on the analytic side of things. This would include lots of techniques discussed by Flajolet and Sedgewick, but would also include things not included in their book (or only mentioned in passing) such as Tauberian theorems and Darboux theorem. It would also probably include a history of the subject including the works of Hardy, Ramanujan, Hayman, etc. I have started an outline here User:Dom_walden/Analytic_combinatorics. This could include a disambiguation header linking to Symbolic_method_(combinatorics) and Analytic_Combinatorics_(book).
• Move Analytic_Combinatorics to Analytic_Combinatorics_(book).
• Leave Symbolic_method_(combinatorics) as it is, but Analytic_combinatorics no longer redirects to it.

@Zaslav @David Eppstein Dom walden (talk) 10:44, 15 October 2023 (UTC)

This is the sensible proposal. The current title of this article is acceptable, but there should be a broad article summarizing the ideas of analytic combinatorics. I do doubt, however, that analytic number theory (Hardy, Ramanujan, et al.) belongs in an article on combinatorics. Zaslav (talk) 22:25, 15 October 2023 (UTC)