Isolated sets of diagonals, diagonal hypergraphs, and simplices of doubly stochastic matrices

Authors: Brualdi, Richard¹; Shao, Jia-Yu²

Source: Linear and Multilinear Algebra, Volume 56, Number 4, July 2008 , pp. 471-480(10)

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Abstract:

We investigate a connection between isolated sets of diagonals of a matrix and simplicial faces of the polytope Ωn of doubly stochastic matrices. We also consider the minimum permanent on simplicial faces of Ωn.

Keywords: Matrix diagonal; Isolated diagonals; Doubly stochastic matrices; Simplex; Permanent; Cohesive; Barycentric

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080701437616

Affiliations: 1: Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA 2: Department of Applied Mathematics, Tongji University, Shanghai 200092, China

Publication date: 2008-07-01