Wikipedia:Reference desk/Archives/Mathematics/2018 November 30

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

November 30

Double exponential function

What's the correct name, double or doubly exponential? Please answer at Talk:Double exponential function#Double or doubly exponential? --CiaPan (talk) 17:51, 30 November 2018 (UTC)

Transversals

I am reading TAOCP vol 4A page 6 where it talks of determining two orthogonal magic latin squares. eg using playing cards with ranks J Q K A and suits S H D C, we could have the rank magic latin square orthogonal to the suit magic latin square:

J A K Q    D H S C    JD AH KS QC
A J Q K    C S H D    AC JS QH KD
K Q J A    H D C S    KH QD JC AS
Q K A J    S C D H    QS KC AD JH

The ranking square can be rewritten using J=0 A=1 K=2 Q=3 as

0 1 2 3
1 0 3 2
2 3 0 1
3 2 1 0

and then, iff the rows are not ordered by the left hand digit we could move rows around to form a magic latin square with top row and left column

0 1 2 3
1 x x x
2 x x x 
3 x x x

but in the example given, it is already in order. An orthogonal magic latin square is a magic latin square such that the combination rank and suit never repeats. In this example we would have somewhere each of the 16 cards

JC QC KC AC  JD QD KD AD  JH QH KH AH  JS QS KS AS

Then we seek an orthogonal magic latin square arbitrarily making the left column the same as the first magic latin square. In the example case we assign suits as D=0 C=1 H=2 S=3, thus getting

0 1 2 3    0 x x x
1 0 3 2    1 x x x
2 3 0 1    2 x x x
3 2 1 0    3 x x x

So now DK casually throws in (for his 10*10 example) that there are 808 transversals being 79 for 0, 96 for 1, 76 for 2, ... 63 for 9. I do not understand why the values are different. I do not understand WHAT a transversal IS - apart from it being a permutation of the N values (0123 in my example). Can anyone explain what is meant? -- SGBailey (talk) 20:47, 30 November 2018 (UTC)

Not that is answers your question, but I'm pretty sure you're talking about Graeco-Latin squares. The article doesn't mention transversals though. --RDBury (talk) 22:46, 30 November 2018 (UTC)

Yes - original Q edited. -- SGBailey (talk) 23:59, 30 November 2018 (UTC)

Ah. I've found good stuff at http://www.karlin.mff.cuni.cz/~loops07/presentations/wanless.pdf -- SGBailey (talk) 08:16, 1 December 2018 (UTC)