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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Nova Southeastern University

2019

Doubly substochastic matrices

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Inequalities For Permanents And Permanental Minors Of Row Substochastic Matrices, Zhi Chen, Jiawei Li, Lizhen Yang, Zelin Zhu, Lei Cao Dec 2019

Inequalities For Permanents And Permanental Minors Of Row Substochastic Matrices, Zhi Chen, Jiawei Li, Lizhen Yang, Zelin Zhu, Lei Cao

Mathematics Faculty Articles

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.


Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li Feb 2019

Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

Mathematics Faculty Articles

Let Ωn denote the convex polytope of all n x n doubly stochastic matrices, and ωn denote the convex polytope of all n x n doubly substochastic matrices. For a matrix A ϵ ωn, define the sub-defect of A to be the smallest integer k such that there exists an (n + k) x (n + k) doubly stochastic matrix containing A as a submatrix. Let ωn,k denote the subset of ωn which contains all doubly substochastic matrices with sub-defect k. For π a permutation of symmetric group of degree …