Minimum permanents on two faces of the polytope of doubly stochastic matrices

Kyle Pula, Seok Zun Song, Ian Murray Wanless

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Abstract

We consider the minimum permanents and minimising matrices on the faces of the polytope of doubly stochastic matrices whose nonzero entries coincide with those of, respectively, U-m,U-n = [(In)(Im,n) (Jn,m)(Om)] and V-m,V-n = ((In)(Jm,n) (Jn,m)(Jm,m)]. Here J(r,s) denotes the r x s matrix all of whose entries are 1, I-n is the identity matrix of order n and O-m is the m x m zero matrix. We conjecture that V-m,V-n is cohesive but not barycentric for 1 <n <m + root m and that it is not cohesive for n >= m + root m. We prove that it is cohesive for 1 <n <m + root m and not cohesive for n 2m and confirm the conjecture computationally for n <2
Original languageEnglish
Pages (from-to)232 - 238
Number of pages7
JournalLinear Algebra and Its Applications
Volume434
Issue number1
DOIs
Publication statusPublished - 2011

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