Minimum permanents on two faces of the polytope of doubly stochastic matrices∗
نویسندگان
چکیده
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, Um,n = [ In Jn,m Jm,n 0m ] and Vm,n = [ In Jn,m Jm,n Jm,m ] . We conjecture that Vm,n 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 6 200. We also show that Um,n is barycentric.
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