We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input variables of the (quasi-polynomial) function are fixed, there is a polynomial time algorithm which converts between the two representations. Examples of such countin...

We use the flux attractor equations to study IIB supergravity compactifications with ISD fluxes. We show that the attractor equations determine not just the values of moduli fields, but also the masses of those moduli and the gravitino. We then show that the flux attractor equations can be recast in terms of derivatives of a single generating function. We also find a simple expression for this ...

We present gauge invariant, self adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multiforms. It also yields explicit action principles for these theories in terms of their minimal covariant field content. For known cases, these actions imply the mixed symmetry equations of motion o...

Periodic orbits are studied using generating functions that yield canonical transformations induced by the phase flow as defined by the Hamilton-Jacobi theory. By posing the problem as a two-point boundary value problem, we are able to develop necessary and sufficient conditions for the existence of periodic orbits of a given period, or going through a given point in space. These conditions red...

Let μ be a probability measure on the real line with finite moments of all orders. Apply Gram-Schmidt orthogonalization process to the system {1, x, · · · , x, . . . } to get a sequence {Pn}∞n=0 of orthogonal polynomials with respect to μ. In this paper we explain a method of deriving a generating function ψ(t, x) for μ. The power series expansion of ψ(t, x) in t produces the explicit form of p...

Generating functions have long been used to analyze properties of sequences of numbers. In this note, we use generating functions to analyze a class of combinatorial objects, called interconnection networks. In particular, we prove that two families of interconnection networks are isomorphic by showing that the corresponding generating functions are isomorphic.