A309257 a(n) is the minimum positive value of the determinants of circulant order n Latin squares.

1, 3, 18, 80, 75, 3087, 196, 1440, 405, 6325, 726, 7488, 1183, 11025, 1800

Offset: 1

Author

Alvaro R. Belmonte, Eugene Fiorini, Peterson Lenard, Froylan Maldonado, Sabrina Traver, Wing Hong Tony Wong, Jul 19 2019

Keywords

• nonn
• more
• hard

Comments

These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019.

Examples

			For n=2, a(2)=3 is the minimum absolute value determinant of a back circulant Latin square of order 2. An example of one such matrix is [[2 1], [1 2]].
For n=5, a(5)= 75 is the minimum absolute value determinant of a back circulant Latin square of order 5. An example of one such matrix is [[1, 2, 4, 5, 3], [3, 1, 2, 4, 5], [5, 3, 1, 2, 4], [4, 5, 3, 1, 2], [2, 4, 5, 3, 1]] has determinant 75.
		

Links

• Froylan Maldonado, Minimum absolute value determinant of back circulant Latin squares code

Crossrefs

Cf. A301371, A308853, A309088, A328062.

Programs

Sage

See Maldonado link.

Extensions

Modified title and a(8)-a(13) from Hugo Pfoertner, Oct 01 2019

a(14) from Hugo Pfoertner, Oct 07 2019

a(15) from Hugo Pfoertner, Oct 13 2019