AbstractLet denote the set of all doubly stochastic matrices of order n. Foregger  raised a n question whether per per (A) holds for all and , where Jn is the n × n matrix with each entry equal to .But this inequality does not hold good for all matrices in general. In this paper, we consider the above inequality for subpermanents and we provide a sufficient condition for a matrix A ∈ Ωn to satisfy the inequality σk(fJn + (1−t)A) ≤ σk(A) for 0 ≤ t ≤ 1 and discuss the consequences of this inequality.
P. Subramanian and Dr. Somasundaram K., “Some Conjectures on Permanents of Doubly Stochastic Matrices”, Journal of Discrete Mathematical Sciences and Cryptography, vol. 19, pp. 997-1011, 2016.