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- 저자 : Pula, K. (검색결과 1 건)
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Minimum permanents on two faces of the polytope of doubly stochastic matrices
Pula, K.,Song, S.Z.,Wanless, I.M. North Holland [etc.] 2011 Linear algebra and its applications Vol.434 No.1
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<SUB>m,n</SUB>=I<SUB>n</SUB>J<SUB>n,m</SUB>J<SUB>m,n</SUB>0<SUB>m</SUB>andV<SUB>m,n</SUB>=I<SUB>n</SUB>J<SUB>n,m</SUB>J<SUB>m,n</SUB>J<SUB>m,m</SUB>. Here J<SUB>r,s</SUB> denotes the rxs matrix all of whose entries are 1, I<SUB>n</SUB> is the identity matrix of order n and 0<SUB>m</SUB> is the mxm zero matrix. We conjecture that V<SUB>m,n</SUB> is cohesive but not barycentric for 1<n<m+m and that it is not cohesive for n≥m+m. We prove that it is cohesive for 1<n<m+m and not cohesive for n≥2m and confirm the conjecture computationally for n<2m≤200. We also show that U<SUB>m,n</SUB> is barycentric.
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