The permanent of an n-square matrix A = (aij) is defined by
where the summation extends over all permutations σ of the symmetric group
Sn. A matrix is said to be a (0, 1)-matrix if each of its
entries is either 0 or 1. A (0, 1)-matrix of n-1 the form , where θj = 0 or 1, j = 1,…, n, and
Pn is the n-square permutation matrix with ones in the (1, 2),
(2, 3),…, (n-1, n), (n, 1) positions, is called a (0, 1)-circulant. Denote
the (0, 1)-circulant . It has
been conjectured that
1