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1964•Canadian Mathematical BulletinOpen access

Permanents of (0, 1)-Circulants

Henryk Minc

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Abstract

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

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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

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Available abstract

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

Key concepts: Circulant matrix, Mathematics, Combinatorics, Square matrix, Permutation matrix, Matrix (chemical analysis), Square (algebra), Symmetric group

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