Permanents of (0, 1)-Circulants

Abstract

The permanent of an n-square matrix A = (a ij ) is defined by where the summation extends over all permutations σ of the symmetric group S n . 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 θ j = 0 or 1, j = 1,…, n, and P n 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