Mathematics Faculty Articles
Document Type
Article
Publication Date
2-2019
Publication Title
Electronic Journal of Linear Algebra
Keywords
Doubly substochastic matrices, Sub-defect, Maximum diagonal sum
ISSN
1081-3810
Volume
35
First Page
45
Last Page
52
Abstract
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 n, the sequence of elements a1π(1); a2π(2), ..., anπ(n) is called the diagonal of A corresponding to π. Let h(A) and l(A) denote the maximum and minimum diagonal sums of A ϵ ωn,k, respectively. In this paper, existing results of h and l functions are extended from Ωn to ωn,k. In addition, an analogue of Sylvesters law of the h function on ωn,k is proved.
Additional Comments
National Natural Science Foundation of China grant #s: 11601233, 11561015; Fundamental Research Funds for the Central Universities grant #: KJQN201718; Natural Science Foundation of Jiangsu Province grant #: BK20160708; Natural Science Foundation of Guangxi Province grant #: 2016GXNSFFA380009
NSUWorks Citation
Cao, Lei; Chen, Zhi; Duan, Xuefeng; Koyuncu, Selcuk; and Li, Huilan, "Diagonal Sums of Doubly Substochastic Matrices" (2019). Mathematics Faculty Articles. 279.
https://nsuworks.nova.edu/math_facarticles/279
ORCID ID
0000-0001-7613-7191
ResearcherID
G-7341-2019
DOI
10.13001/1081-3810.3760
Comments
This Article is brought to you for free and open access by Wyoming Scholars Repository. It has been accepted for inclusion in Electronic Journal of Linear Algebra by an authorized editor of Wyoming Scholars Repository.