A111749 Number of (-1,0,1) periodic irreducible matrices (with Tij = -Tji for i < j) up to sign change, transposition and row and column permutations.

1, 3, 10, 39, 121, 405

Offset: 1

Author

Wouter Meeussen, Nov 19 2005

Keywords

• nonn
• hard
• more

Comments

The permutations of rows i and j, followed by those of column i and j, preserve the property that (Tij = -Tji for i < j). The periods of the 405 6 X 6 matrices are: 11 times period 3, 94 times period 4, 71 times period 6 and 229 times period 12.

Examples

			{{-1,-1,0,0,0,0}, {1,1,-1,0,0,0}, {0,1,-1,0,0,0}, {0,0,0,-1,-1,0}, {0,0,0,1,1,-1}, {0,0,0,0,1,-1}} is one of the 6 X 6 matrices.
		

Links

• Wouter Meeussen, Periodic Matrices. [broken link]

Crossrefs

Cf. A072148, A111485.

Programs

Mathematica

(* See link. *)