A328062 - OEIS

%I #11 Oct 13 2019 14:05:22

%S 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,

%T 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,

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

%N 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.

%H Hugo Pfoertner, <a href="/A328062/b328062.txt">Table of n, a(n) for n = 1..120</a>, rows 1..15 of triangle, flattened

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.

%e The triangle starts

%e   1;

%e   2,  1;

%e   1,  2,  3;

%e   3,  1,  4,  2;

%e   1,  2,  4,  5,  3;

%e   1,  2,  4,  5,  6,  3;

%e   1,  2,  4,  6,  7,  5,  3;

%e   3,  1,  5,  4,  8,  6,  7,  2;

%e   1,  2,  4,  6,  8,  9,  7,  5,  3;

%e   5,  1,  7,  3,  8,  4, 10,  6,  9,  2;

%e .

%e 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.

%e   [3, 1, 4, 2;

%e    2, 3, 1, 4;

%e    4, 2, 3, 1;

%e    1, 4, 2, 3].

%e 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.

%Y Cf. A309257, A328029, A328030.

%K nonn,tabl

%O 1,2

%A _Hugo Pfoertner_, Oct 03 2019