On assignment functions

Abstract

We define a class of functions called assignment functions, one of which is the permanent function. These functions evaluated at matrices of 0's and 1's are shown to be of applied and combinational interest. We define assignment polytopes which generalize the classical assignment polytope and use them to obtain bounds for the assignment function. We propose the determination of the minimum and maximum value of an assignment function on its corresponding assignment polytope and conjecture that the maximum value is 1. A natural conjecture for the minimum value is shown to be false. The minimum and maximum value are determined for special assignment functions.