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

1,2

Comments

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

Links

Table of n, a(n) for n=1..15.

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

Example

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.

Prog

(Sage) See Maldonado link.

Crossrefs

Cf. A301371, A308853, A309088, A328062.

Sequence in context: A056310 A309259 A308853 * A135371 A086346 A337193

Adjacent sequences: A309254 A309255 A309256 * A309258 A309259 A309260

Keyword

nonn,more,hard

Author

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

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

Status

approved