A328062 Lexicographically earliest permutation of [1,2,...,n] minimizing the positive value of the determinant of an n X n circulant matrix that uses this permutation as first row, written as triangle T(n,k), k <= n.

1, 2, 1, 1, 2, 3, 3, 1, 4, 2, 1, 2, 4, 5, 3, 1, 2, 4, 5, 6, 3, 1, 2, 4, 6, 7, 5, 3, 3, 1, 5, 4, 8, 6, 7, 2, 1, 2, 4, 6, 8, 9, 7, 5, 3, 5, 1, 7, 3, 8, 4, 10, 6, 9, 2, 1, 2, 3, 8, 6, 4, 9, 10, 11, 5, 7, 3, 1, 5, 4, 9, 8, 12, 10, 11, 6, 7, 2, 1, 2, 3, 5, 8, 7, 6, 9, 11, 12, 13, 10, 4

Offset

1,2

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..120, rows 1..15 of triangle, flattened

Wikipedia, Circulant matrix.

Example

The triangle starts
  1;
  2,  1;
  1,  2,  3;
  3,  1,  4,  2;
  1,  2,  4,  5,  3;
  1,  2,  4,  5,  6,  3;
  1,  2,  4,  6,  7,  5,  3;
  3,  1,  5,  4,  8,  6,  7,  2;
  1,  2,  4,  6,  8,  9,  7,  5,  3;
  5,  1,  7,  3,  8,  4, 10,  6,  9,  2;
.
The 4th row of the triangle T(4,1)..T(4,4) = a(7)..a(10) is [3,1,4,2] because this is the lexicographically earliest permutation of [1,2,3,4] producing a circulant 4 X 4 matrix with minimum positive determinant A309257(4) = 80.
  [3, 1, 4, 2;
   2, 3, 1, 4;
   4, 2, 3, 1;
   1, 4, 2, 3].
All lexicographically earlier permutations lead to the other possible determinants -160, -80, 0, 160 with [1,3,2,4], [1,4,3,2], [2,3,1,4], and [2,4,1,3] producing determinants = -80.

Crossrefs

Cf. A309257, A328029, A328030.

Sequence in context: A153734 A285554 A128495 * A326281 A343026 A113136

Adjacent sequences: A328059 A328060 A328061 * A328063 A328064 A328065

Keyword

nonn,tabl

Author

Hugo Pfoertner, Oct 03 2019

Status

approved