Talk:Latin square

message: I added a paragraph on a mathematical puzzle that illustrates a generalized version of Latin-square orthogonality. Cullinane 17:33, 14 August 2005 (UTC)
thread_title: Latin squares and mathematical puzzles

message: Doesn't the name Latin Square originate from the ?first known example (from Roman times), namely the word square Sator Arepo Tenet Opera Rotas? Ben Finn 16:39, 2 April 2006 (UTC)
replies: text: No, that is not a Latin square in the meaning of this article. For example, it has no "T" in the second row. As far as I have heard, the earliest known Latin squares appeared in Arabic manuscripts around the 12th century; this needs to be researched and put in the article.  The name "Latin square" was coined by Euler in his paper of 1782 with a rather weak justification: he used Latin letters as the symbols. McKay 07:19, 17 May 2006 (UTC)

text: The French version of the name, "le quarré latin" is used near the bottom of page 90 of Euler's 1782 paper, and again towards the top of page 91. I don't think we need to ascribe its coinage to later authors. —David Eppstein (talk) 00:19, 22 May 2021 (UTC)
thread_title: Name

message: The correct value is 564, not 563.  See  for the history of this error.  This is accepted by Colbourn and Dinitz.  --McKay 07:29, 12 April 2006 (UTC)
thread_title:  Isotopy classes of order 7 

message: If all Latin squares can be reduced, does this not mean that every quasigroup is a loop? —The preceding unsigned comment was added by 149.135.97.128 (talk) 11:08, 10 January 2007 (UTC)
replies: text: No.  The operations which can be used to reduce a Latin square (permutation of the rows and columns) change the quasigroup to a different quasigroup.  These operations are called isotopies, so the conclusion is that every quasigroup is isotopic to a loop.  It is not true that every quasigroup is a loop. McKay 02:40, 11 January 2007 (UTC)
thread_title:  Question 

message: I might be missing something, but shouldn't the article include a note (or a section) about the relation of Latin squares to projective (or affine) planes?
Denes and Keedwell show a proof of this in "Latin Squares and Their Applications" (although I don't think the proof is theirs).
Gal Diskin —The preceding unsigned comment was added by 85.65.215.115 (talk) 17:23, 11 January 2007 (UTC)
thread_title:  Latin Squares and projective \ affine planes 

message: This note is a reminder for me and others that it might be worthwhile to include something about Orthogonal latin squares, as detailed e.g in . The problem of constructing such matrixes and especially the impossible 6x6 matrix problem has been popularized in a number of books and articles and might make a good read. 
Also, in the section about error correcting codes, I committed the sin of writing "orthogonal latin squares" without defining what it means. :-] EverGreg 15:34, 13 May 2007 (UTC)
thread_title:  Orthogonal Latin Squares

message: The article states, in its first reference to orthogonal Latin squares:
"Sets of Latin squares that are orthogonal to each other have found an application as error correcting codes in situations where communication is disturbed by more types of noise than simple white noise, such as when attempting to transmit broadband internet over powerlines. [1] [2] [3]"
Unfortunately, the word orthogonal in this sense has *not* been defined previously, which makes this mention of the word orthogonal inappropriate.  Further, the word "orthogonal" *has* been used previously (unnecessarily, in my opinion) to discuss the simple ordinary representation of a Latin square as a matrix, which the article somehow feels the need to refer to as an "orthogonal array".
It is certainly a good idea to discuss orthogonal Latin squares in this article, but this must be done in such a way that the concept is defined and the terminology is clear before it starts to be used without definition.
I hope this problem can be fixed.Daqu (talk) 22:44, 20 February 2009 (UTC)
replies: text: Eleven years later (!!), I've added a link to the article on orthogonal Latin squares. Joriki (talk) 18:40, 23 March 2020 (UTC)
thread_title: Problem with mention of orthogonal Latin squares

message: I came here looking for how Latin squares are used in experimental design.  It's mentioned in the intro, but I wonder if an expert could add a paragraph under applications.  I'm at a conference and a lot of people have mentioned how they used Latin squares for randomizing their experiments, and I don't know what they mean, so I thought that might be a good thing to have here. Thanks 209.255.241.2 (talk) 16:54, 25 March 2010 (UTC)
replies: text: You've got a good point. Information on this is rather fragmented on wikipedia. OK starting points are Blocking (statistics), Randomized block design and especially Hyper-Graeco-Latin square design. The bigger picture may perhaps be found in Design of experiments. None of these are the readable introductions they should have been, but hopefully they work as pointers to further reading in the literature. The gist of it is that when you do an experiment where say four variables can each take two values (high/low) you want to try every possible combination but there may not be time or money to do that. So you want to get as much info with as few experiments as possible. First you ofcourse avoid doing the same experiment twice, but you also want to avoid that two of your variables change in lockstep in each experiment, because then you wouldn't have been able to tell their effects apart. Following a latin square is one way to design a good set of experiments. EverGreg (talk) 18:17, 25 March 2010 (UTC)
replies: text:  I'll start adding some references on Latin squares here. When I'm done, I'll update the article. Kiefer.Wolfowitz (talk) 20:22, 22 May 2010 (UTC)
thread_title: Applications for experimental design

message: An anonymous user proposed a merger. It seems straightforward to me to put Graeco-Latin square as a chapter of Latin square. 
In addition: As the previous discussions on this page shows, it's a problem that orthogonal latin squares are not properly defined here, they seem to tie in closely with the text. The Graeco-Latin article seems to go a long way in defining it, so this could be a good start, though the text in the Graeco-Latin article is less accessible than that of Latin square. (That is, I still don't know what "a orthogonal latin square" is, and barely what two mutually orthogonal ones are.) EverGreg (talk) 22:10, 5 April 2010 (UTC)
replies: text: Don't merge  There are enough subtopics of Latin square to need different articles.  A basic Latin square is essentially about one factor in addition to rows or columns, a Graeco-Latin square about two or more.  As for orthogonal Latin squares, they have to come in comparison of pairs: there must be at least one cell (and so implicitly exactly one out of the n2 cells) which has any particular combination of the n posible values of each of the two symbols being considered.--Rumping (talk) 16:41, 22 July 2010 (UTC)
replies: text: Due to the fact that no agreement has been reached — and only two comments — in eight months, I am removing the merge templates from each page. Supertouch (talk) 00:31, 4 November 2010 (UTC)
thread_title: Merger proposal

message: The examples for the two latin squares of order 5 at the end of the text are from the same main class.
Correct representatives for the two main classes are given at http://cs.anu.edu.au/~bdm/data/latin.html .
In one of the main classes, all ordered pairs of numbers must be at most once within the square, none of the currently given squares have this property.Random rings (talk) 12:45, 4 June 2010 (UTC)
thread_title:  Error in example 

message: It says" the orthogonal array representation of the first Latin square displayed above is:"
But this example refers to a square with numbers which is not displayed in the article.(maybe it has been edited out at some time)
Should we change this to (1,1,A), (1,2,B) and so on? Or put back the original figure.
The whole expression "the first latin square displayed above" is also a bit vague. (figure number nn might be better?)Bj norge (talk) 19:00, 14 April 2011 (UTC)
thread_title:  Orthogonal array representation (refers to non-existing figure) 

message: Questions:
1. There are four frequencies and four time slots. What then is the meaning of 'the letter A would then be picked up as: 12 12 123 124'?
2. 'But the 1,2 case is the only one that yields a sequence matching a letter in the above table...'. Should it read  'sequence' instead of 'case'?
3. 'Again, we are able to infer from the table of encodings that it must have been the letter A being transmitted.' Is it too much to spell out *why* we are able to infer this?  — Preceding unsigned comment added by Polariseke (talk • contribs) 15:54, 24 February 2012 (UTC)
thread_title:  Error Correction Codes Example Unclear 

message: Can I show my formula for computing the total number of Latin Squares? It isn't a research idea. I just saw how to compute them and I thought that someone should know. It took me about 10 minutes. It isn't correct to say that no known formula exists. You can contact me at leavemsg1@gmail.com Bill Bouris 67.184.226.32 (talk) 15:54, 23 May 2015 (UTC)
replies: text: No, wikipedia is not an appropriate venue for publishing original research.  You can see our policy on this here: WP:OR.  In the (unlikely) event that you are correct, you should write it up for publication in an appropriate peer-reviewed journal.  --JBL (talk) 16:08, 23 May 2015 (UTC)
replies: text:  It's too bad that someone is in charge of such a wonderful venue. My idea is very sound, and what would make it unlikely? There isn't the need for a peer to review anything that's just pure algebra. Oh well... JBL doubts my autistic ability, so the rest of you will just suffer! 108.242.169.13 (talk) 17:45, 23 May 2015 (UTC)
replies: text:  You might try the Math Reference Desk if you're looking for someone to discuss mathematics with.  This is not the appropriate venue.  --JBL (talk) 19:40, 23 May 2015 (UTC)

text: "Not easily computable" is, if anything, a major understatement.  --JBL (talk) 23:42, 9 September 2015 (UTC)

text: On the other hand, here's a great survey article on counting Latin squares and rectangles.  It includes some form of the formula you mention (with two citations, including this one) and much more. --JBL (talk) 23:59, 9 September 2015 (UTC)
replies: text:  A formula is useless unless the meaning of the symbols in it is explained. McKay (talk) 03:11, 10 September 2015 (UTC)
replies: text: Agreed, so I put the definitions in. If we are going to do this, then I think we should put all the explicit formulas mentioned in Joel's reference into the article with the proper attributions. The section would also need a bit of a rewrite since the first sentence seems to contradict the existence of explicit formulae. As this is a computability question, I'm a little out of my depth and hope that someone else can put this together. Bill Cherowitzo  (talk) 03:50, 10 September 2015 (UTC)
thread_title:  formula for computing total number of Latin Squares 

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thread_title:  External links modified 

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