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A central limit theorem for integer partitions into small powers.

Gabriel F Lipnik1, Manfred G Madritsch2, Robert F Tichy1

  • 1Institute of Analysis and Number Theory, Graz University of Technology, 8010 Graz, Austria.

Monatshefte Fur Mathematik
|January 15, 2024
PubMed
Summary
This summary is machine-generated.

This study explores integer partitions with specific constraints, proving a central limit theorem for the number of parts. The research utilizes the saddle-point method for analysis.

Keywords:
Central limit theoremInteger partitionsMellin transformPartition functionSaddle-point method

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Area of Science:

  • Number Theory
  • Combinatorics
  • Mathematical Analysis

Background:

  • The partition function p(n) counts integer solutions to n = sum of positive integers.
  • Integer partitions are fundamental in number theory and combinatorics.

Purpose of the Study:

  • Investigate a variant of integer partitions with restricted summands.
  • Analyze the distribution of the number of summands in these restricted partitions.

Main Methods:

  • Application of the saddle-point method.
  • Asymptotic analysis of partition functions.

Main Results:

  • Establishment of a central limit theorem for the number of summands in the studied partition variant.
  • Characterization of the asymptotic behavior of these partitions.

Conclusions:

  • The study provides new insights into the structure of restricted integer partitions.
  • The findings contribute to the understanding of partition function distributions through advanced analytical techniques.