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Minimizing the Permanent over Some Faces of the Polytope of Doubly Stochastic Matrices
Hwan, Suk-Eeun 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.2 No.-
We determine the minimum permanents and minimizing matrices over certain faces of the polytope of doubly stochastic matrices.
A Face of the Polytope of Doubly Stochastic Matrices Associated with Certain Matrix Expansions
Hwang, Suk-Eeun,Shin, Sun-Jeong 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.5 No.-
We generalize the notion of the staircase matrices and deal with the problem of minimizing the permanent over faces, determined by this ‘generalized staircase’ matrices, of the polytope Ω_(n) consisting of all n×n doubly stochastic matrices.
n the spectral radius of (0, 1)-matrices with 1's in prescribecl positions
Brualdi, Richard A.,Huang, Suk-Eeun 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.5 No.-
Let n and d be positive integers with 1≤d≤n(n-1)/2. We investigate the maximum and minimum spectral radius of a (0,1)-matrix of order n which has 1's on and below its main diagonal and d additional 1's. If d≤4 we determine all matrices of this type which have the maximum spectral radius. For general d we prove an asymptotic results that severely limits the structure of matrices with maximum spectral radius. For d≤n, we determine the minimum spectral radius.
Vector Majorization via Hessenberg Matrices
Brualdi, Richard A.,Hwang, Suk-Eeun 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.5 No.-
In this paper, it is proved that, for real n-vectors x and y, x is majorized by y if and only if x=PHQy for some permutation matrices P, Q and for some doubly stochastic matrix H which is a direct sum of doubly stochastic Hessenberg matrices. This result reveals that any n-vector which is majorized by a vector y can be expressed as a convex combination of at most (n^2 - n + 2) / 2 permutations of y.
Certain Nonbarycentric Cohesive Matrices
Fischer, Ismor,Hwang, Suk-Eeun 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.5 No.-
Let P_(n) denote the permutation matrix corresponding to the n-cycle (1 2 … n) and let K_(2) denote the 2×2 matrix of l's. In this paper we investigate the permanent minimization problem over the face determined by (I_n+P_n)??K_(2) of the polytope of n×n doubly stochastic matrices, with which we also answer a couple of open questions in the theory of permanents.