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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
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
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 …