Study of the permanent conjecture and some of its generalizations. II
Abstract: In this paper we investigate in a more systematic manner some of the topics initiated in part I of the paper with same title . More specifically, we study in greater detail the properties of the function defined in  attached to convex polytopes, whose properties in the special case of the space of doubly stochastic matrices are connected with the permanent conjecture. Some close links with Perron-Frobenius theory are developed, and we obtain as a by-product of our study what is, I believe, a new expression for the maximum eigenvalue of a nonnegative matrix, which leads to some new estimates of the same. A final section of the paper investigates some purely algebraic properties of , and we obtain some very interesting information connecting a doubly stochastic matrix and its transversals.
In order to keep this paper as self-contained as possible, facts used here drawn from part I are stated with as much explicit detail as possible.
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