An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by theâ€¦ (More)

The object of this note is to state certain theorems, whose proofs together with related results will appear elsewhere. The theorems are mainly concerned with asymptotic enumeration of theâ€¦ (More)

We study a special partial fraction technique which is designed for rational functions with poles on the unit circle, known as q-fractions. Even though the theory of q-partial fractions has alreadyâ€¦ (More)

This work is motivated by Nathansonâ€™s recent paper on relatively prime sets and a phi function for subsets of {1, 2, 3, . . . , n}. We establish enumeration formulas for the number of relativelyâ€¦ (More)

Let G, denote the multiplicative semigroup of all monk polynomials in one indeterminate over a tinite field F, with q elements. By a direct fhctor of G, is understood a subset E, of G, such that, forâ€¦ (More)

(cf. [8], say). Atiyah [ l ] posed the problem of relating the Chern classes of i{K with those of X, for any representation X of H. The purpose of this note is to announce the proof of a conjectureâ€¦ (More)

In this paper, we consider a two-dimensional model for finite set partitions which arises in conjunction with a special case of a general non-linear recurrence. We investigate properties of some ofâ€¦ (More)

An algorithm is introduced and shown to lead to a unique infinite product representation for a given formal power series A(z) with A(O)= 1. The infinite product is 1; n (1 + b,z'n)> " =I