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

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=InJn,mJm,n0mandVm,n=InJn,mJm,nJm,m.Here Jr,sJr,s denotes the r×sr×s matrix all of whose entries are 1, InIn is the identity matrix of order n   and 0m0m is the m×mm×m zero matrix.We conjecture that Vm,nVm,n is cohesive but not barycentric for 1