Detailed asymptotic expansions for partitions into powers

2022/05/26 by Cormac O’Sullivan, O'Sullivan, Cormac · 1 citation
Mathematics · #05A17 #11P82 #41A60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2205.13468

openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we examine the number of ways to partition an integer n into kth powers when n is large. Simplified proofs of some asymptotic results of Wright are given using the saddle-point method, including exact formulas for the expansion coefficients. The convexity and log-concavity of these partitions is shown for large n, and the stronger conjectures of Ulas are proved. The asymptotics of Wright's generalized Bessel functions are also treated.

Cited by

• Asymptotics of the shifted finite differences of the overpatition function and a problem of Wang--Xie--Zhang

Related

• Power partitions and saddle-point method
• Power Partitions
• Error bounds for the asymptotic expansion of the partition function
• Partitions into prime powers
• An expansion for the number of partitions of an integer