In optimization problems such as integer programs or their relaxations, one encounters feasible regions of the form {x ∈ R+ : Rx ∈ S} where R is a general real matrix and S ⊂ R is a specific closed set with 0 / ∈ S. For example, in a relaxation of integer programs introduced in [ALWW2007], S is of the form Z − b where b 6∈ Z . One would like to generate valid inequalities that cut off the infea...

Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, classical generating functions that define unitary operators are discussed. Next, group theoretical approach to generating functions that have unitar...

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with speci c properties, and that every function with these speci c properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized b...

1 Generating Functions 1.1 The ordinary generating function We define the ordinary generating function of a sequence. This is by far the most common type of generating function and the adjective “ordinary” is usually not used. But we will need a different type of generating function below (the exponential generating function) so we have added the adjective “ordinary” for this first type of gene...