Publication Type:

Journal Article

Source:

Journal of Discrete Mathematical Sciences and Cryptography, Volume 19, Number 5-6, p.997-1011 (2016)

URL:

http://dx.doi.org/10.1080/09720529.2015.1130813

Keywords:

Doubly stochastic matrix, Permanents, Subpermanents AMS Subject classification: 15A15

Abstract:

AbstractLet denote the set of all doubly stochastic matrices of order n. Foregger [3] 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.

Cite this Research Publication

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.