Perron eigenvectors and the symmetric transportation polytope (Q1174689)

Given two positive \(n\) vectors \(x\) and \(y\) the structure of the convex polytope of all nonnegative matrices \(C\) for which \(Cx = x\) and \(y^ \top C = y^ \top\) is investigated. By a diagonal transform the polytope is transformed into the set of all nonnegative matrices \(A\) such that \(A e_ n = z \text{\;and\;} e^ \top_ n A = z^ \top\) where \(e_ n = (1, \dots, 1)^ \top\) and \(z\) is a given positive vector. This symmetric transportation polytope is studied as a function of \(z\). Bounds for the number of extreme points are given and vectors \(z\) characterized for which this number attains its maximum.