Let Ωn denote the set of all n × n doubly stochastic matrices. Two unequal matrices A and B in Ωn are called permanental mates if the permanent function is constant on the line segment t A + (1 - t) B, 0 ≤ t ≤ 1, connecting A and B. We study the perturbation matrix A + E of a symmetric matrix A in Ωn as a permanental mate of A. Also we show an example to disprove Hwang's conjecture, which states that, for n ≥ 4, any matrix in the interior of Ωn has no permanental mate. © 2007 Elsevier Ltd. All rights reserved.
cited By (since 1996)1
SaMaria Arulraj and Dr. Somasundaram K., “Permanental Mates: Perturbations and Hwang's conjecture”, Applied Mathematics Letters, vol. 21, pp. 786-790, 2008.