Talk:Domino tiling

Further to the article analysis conducted by Propaniac, this article has been improved through addition and clarification by both Giftlite and ZICO. I submit that this article is notable and should be included in Wikipedia for a number of reasons:


 * 1. There is no other article concerning the number 12988816 (known to me).
 * 2. This article is genuinely useful for reference purposes.
 * 3. There are many articles similar to this one, which are also useful for reference. For a typical example, the article for the number 495 may be viewed.
 * 4. Professor Michael E. Fisher is an excellent, notable scientist and is a recipient of the Wolf Prize, the Boltzmann Medal and the Lars Onsager prize. Some of this article concerns some of his work.
 * 5. The Pfaffian calculation method mentioned in the article is a very useful one, applicable to a very wide range of subjects.
 * 6. The number 12988816 is the answer to a very common example problem designed for solution by the Pfaffian method.

My thanks to Propaniac for his analysis, ZICO 19:08, 12 April 2007 (UTC).


 * Thanks (sincerely) for offering this defense. My main objection to this number as an article subject is that I can think of no way that anybody would ever decide to look up the number 12988816 to find out more information about it. I don't object (in theory, anyway) to Wikipedia containing information about the Pfaffian method, or about this particular problem, or Michael E. Fisher and his work. But it does not make sense to me that there should be an article for a number that is only notable as the answer to a math problem. Both the article and the external reference provided seem to be about the problem and not about the number itself.
 * Also, while there are quite a few number articles that aren't justified in my opinion, "there are other articles like this" is not generally considered a valid argument for or against deletion. Propaniac 20:03, 12 April 2007 (UTC)


 * Thanks for your response. I address your arguments as follows:


 * With regards to looking up the number, I could imagine the article "12988816" used more as a reference from another Wikipedia article than simply as an article one might look up directly (as a search). I would normally come to the conclusion that the number (and information concerning it) should simply be added as additional information to the article in question (the article that would reference the number's article), however, I had occasion to actually look up "12988816" (in an attempt to find out more information on the number), so, it seemed reasonable to assume that if I searched for the number, then it would be very likely that there would be someone else who might do the same.


 * What would your views be on adding a reference link for "12988816" (linking to the number's separate article) to the "Pfaffian" article, together, of course, with a short explaination for the number?


 * With regards to having the number notable as simply the answer to a math problem, the main known reason for the notability of the number is, indeed, the fact that it is the solution to the basic problem given, thus, it makes sense to include some (minimal) details of the actual problem that makes the number notable in the article, with appropriate references to the more detailed article concerning the Pfaffian method.


 * I reviewed the Wikipedia article on the notability of numbers. One quote from the article is the following:


 * "...highly composite numbers are notable enough to get their own article since they were studied by Paul Erdős"


 * It is assumed from this statement that a number can be considered notable in Wikipedia by association with a notable person. While I don't really agree with this rationale, if I am to go by it, then an article for 12988816 is justified by the number's association with not one, but three notable people (one of which has a Wikipedia article etc).


 * With regards to the "there are other articles like this" argument, my point was, in fact, that there are similar articles which are useful for reference. I was trying to demonstrate that this article is useful for reference purposes (it is the answer to a very common example problem. I take your point on this, though.


 * I honestly think that the addition of this article can only help make Wikipedia more useful and that the benefits of having the article outweigh the drawbacks. Further, the article itself could be used as the location to place more information on the number (existing information and information yet to be discovered).


 * P.S.
 * I added a reference to the page. This reference gives direct information about the number, as per your suggestion.


 * P.P.S.
 * It is very refreshing to talk with someone with good grammar!


 * Thanks again for your input! ZICO 00:07, 13 April 2007 (UTC)

OEIS template?
Does anyone know how OEIS is supposed to work? I used it in the EL section, but it's not what I expected. -- Mikeblas 17:35, 17 April 2007 (UTC)

Result for an n-by-n checkerboard
It strikes me that this paragraph:

More generally, the number of ways to cover a $$ 2n $$-by-$$ 2n $$ square with $$ 2n^2 $$ dominoes (as calculated independently by Temperley and M.E. Fisher and Kasteleyn in 1961) is given by


 * $$ \prod_{j=1}^N \prod_{k=1}^N \left ( 4\cos^2 \frac{\pi j}{2n + 1} + 4\cos^2 \frac{\pi k}{2n + 1} \right ) $$

The calculation of the number of possible ways of tiling a standard chessboard with 32 dominoes is a simple, commonly used, example of a problem which may be solved through the use of the Pfaffian technique. This technique may be applied in many mathematics-related subjects, for example, in the classical, 2-dimensional computation of the dimer-dimer correlator function in quantum mechanics.

really belongs in another article. That is, this is not information about the number 12988816; it is information about an application of the Pfaffian technique. Unless someone strongly objects (a reasoned objection), I plan to remove the paragraph here and merge it into the Pfaffian article. Lunch 21:48, 17 April 2007 (UTC)

Chapman reference
I'm removing the reference

Robin Chapman was kind enough to email me the document in question. It is a single-paragraph letter to the editor, in response to a previous article by George Jellis examining recurrence formuale for tilings of rectangles of width up to four. The letter points out that the problem of counting domino tilings of rectangles had already been completely solved by Kasteleyn and repeats Kasteleyn's formula. So it's not an actual paper and it doesn't really add anything to the material we alreeady cite from other sources. —David Eppstein (talk) 15:23, 9 June 2008 (UTC)