Gaussian Polynomials and Restricted Partition Functions with Constraints

TL;DR

This paper presents an explicit formula for a restricted partition function with constraints, building on known expressions for an unconstrained version, advancing the understanding of partition functions under restrictions.

Contribution

It introduces a new explicit formula for constrained partition functions based on existing formulas for unconstrained cases.

Findings

Derived an explicit formula for P_n^m(s) with constraints

Connected constrained and unconstrained partition functions

Enhanced computational methods for restricted partitions

Abstract

We derive an explicit formula for a restricted partition function P_n^m(s) with constraints making use of known expression for a restricted partition function W_m(s) without constraints