On partition polynomials and partition functions

TL;DR

This paper revisits Bell's work on partition polynomials, introduces reciprocal partition polynomials with explicit formulas, and applies these to derive closed-form expressions for various partition functions.

Contribution

It introduces reciprocal partition polynomials and provides explicit formulas, expanding the theoretical framework for partition functions.

Findings

Derived explicit formulas for reciprocal partition polynomials

Computed closed-form expressions for well-known partition functions

Extended Bell's work on partition polynomials

Abstract

In this paper we revisit the work of E.T. Bell concerning partition polynomials in order to introduce the reciprocal partition polynomials. We give their explicit formulas and apply the result to compute closed formulae for some well-known partition functions.