Talk:Mutually orthogonal Latin squares

message: More information on context and application would be helpful Calaf 02:03, 28 February 2007 (UTC)
replies: text: I certainly don't think it is - and the article is 260k long! I think a link to the solutions would be more apt. --moof (talk) 08:50, 10 April 2009 (UTC)
replies: text: I've informed the editor at User talk:Brhaspati.  The size is just too big.  I'll suggest using the main 144 solutions, and cut out the other 7 x 144 transpostions, reflections, etc.  But even that might keep the article at too big a size.  Smallbones (talk) 13:10, 21 April 2009 (UTC)
replies: text: I'm OK with pruning the list, but not with reducing them to the 144 solutions in the first column -- that would be neither complete (which is what it is now) nor instructive. An instructive reduction would be to reduce the 1152 to just 2 cases and show how the rest of the 1152 can be derived from them using permutations of suits and face values. I'll do this in a few hours. -- Brhaspati\talk/contribs 23:13, 21 April 2009 (UTC)

text: Yes, it looks like what is meant by an 'equivalence class' here needs clarifying: the second "distinct" solution is obtainable from the first by reflecting across the principal diagonal and applying the permutation (JKQ)*(♦♥♣). Am I missing something here? Pirate pete (talk)  —Preceding undated comment added 13:10, 9 May 2018 (UTC)

message: If I have n2 things, I want to part them to n sets k times, and any two things are in different sets every times, what is the maximal value of k?
When n = 0 or n = 1, it is infinite.
When n = 2, I can part them like this:
{AB, CD}, {AC, BD}, {AD, BC}
Thus, the maximal value of k is 3.
When n = 3, I can part them like this:
{ABC, DEF, GHI}, {ADG, BEH, CFI}, {AEI, BFG, CDH}, {AFH, BDI, CEG}
Thus, the maximal value of k is 4.
When n = 4, I can part them like this:
{ABCD, EFGH, IJKL, MNOP}, {AEIM, BFJN, CGKO, DHLP}, {AFKP, BELO, CHIN, DGJM}, {AGLN, BHKM, CEJP, DFIO}, {AHJO, BGIP, CFLM, DEKN}
Thus, the maximal value of k is 5.
This is known when n ≥ 2, then k ≤ n+1.  — Preceding unsigned comment added by 49.214.225.38 (talk) 15:07, 12 August 2016 (UTC)
thread_title:  A related problem 

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message: Donald Knuth found exmamples of orthogonal latin squares used by a 14th-century Maghreb mysticist.  See [].  AmirOnWiki (talk) 18:47, 4 January 2021 (UTC)
thread_title:  Medieval reference 

message: This is an obvious question whose answer may be already contained in the article.
But it is not at all clear how to extract this information without reading and fully understanding the entire article.
Suggestion: I hope someone knowledgeable about this subject can add a section containing what is known about the obvious question: 
    For which N does there exist an N×N Graeco-Latin square?
2601:200:C000:1A0:C17A:92A9:4C4E:C680 (talk) 13:27, 31 March 2021 (UTC)
replies: text: For all n > 2 except n = 6. See Euler's conjecture and disproof. —Dexxor (talk) 19:28, 31 March 2021 (UTC)
thread_title:  For which N does there exist an N×N Graeco-Latin square?