Publication Type : Journal Article
Publisher : Journal of Discrete Mathematical Sciences and Cryptography.
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
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Year : 2016
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.