A general asymptotic formula for distinct partitions

TL;DR

This paper develops a broad asymptotic formula for counting distinct integer partitions, extending previous formulas to wider parameter ranges and unifying known results as special cases.

Contribution

It introduces a general asymptotic formula for distinct partitions valid over a broader parameter space than existing formulas.

Findings

Derived a new asymptotic formula for distinct partitions

Unifies previous asymptotic results as special cases

Extends validity range of asymptotic formulas

Abstract

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is valid for any value of the number of parts. We obtain general asymptotic formulas for distinct partitions that are valid in a wider range of parameters than the existing asymptotic formulas, and we recover the known asymptotic results as special cases of our general formulas.