login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309985 Maximum determinant of an n X n Latin square. 8
1, 1, 3, 18, 160, 2325, 41895, 961772, 26978400, 929587995 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A301371(n) for n <= 7. a(8) < A301371(8) = 27296640. It is unknown whether this continues for n > 8.

a(10) = 36843728625, conjectured. See Stack Exchange link. - Hugo Pfoertner, Sep 29 2019

LINKS

Table of n, a(n) for n=0..9.

Brendan McKay, Latin squares.

Mathematics Stack Exchange, Maximum determinant of Latin squares, (2014), (2016).

EXAMPLE

An example of an 8 X 8 Latin square with maximum determinant is

  [7  1  3  4  8  2  5  6]

  [1  7  4  3  6  5  2  8]

  [3  4  1  7  2  6  8  5]

  [4  3  7  1  5  8  6  2]

  [8  6  2  5  4  7  1  3]

  [2  5  6  8  7  3  4  1]

  [5  2  8  6  1  4  3  7]

  [6  8  5  2  3  1  7  4].

An example of a 9 X 9 Latin square with maximum determinant is

  [9  4  3  8  1  5  2  6  7]

  [3  9  8  5  4  6  1  7  2]

  [4  1  9  3  2  8  7  5  6]

  [1  2  4  9  7  3  6  8  5]

  [8  3  5  6  9  7  4  2  1]

  [2  7  1  4  6  9  5  3  8]

  [5  8  6  7  3  2  9  1  4]

  [7  6  2  1  5  4  8  9  3]

  [6  5  7  2  8  1  3  4  9].

CROSSREFS

Cf. A040082, A301371, A308853, A309258, A309984.

Sequence in context: A067302 A212599 A052182 * A328030 A301371 A115415

Adjacent sequences:  A309982 A309983 A309984 * A309986 A309987 A309988

KEYWORD

nonn,more,hard

AUTHOR

Hugo Pfoertner, Aug 26 2019

EXTENSIONS

a(9) from Hugo Pfoertner, Aug 30 2019

a(0)=1 prepended by Alois P. Heinz, Oct 02 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)