Formulæ for the Number of Partitions of n into at Most m Parts (Using the Quazi-Polynomial Ansatz)

Authors

Andrew Sills, Georgia Southern UniversityFollow
Doron Zeilberger, Rutgers UniversityFollow

Document Type

Article

Publication Date

5-2012

Publication Title

Advances in Applied Mathematics

DOI

10.1016/j.aam.2011.12.003

ISSN

0196-8858

Abstract

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for p_m(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the author must have permission to distribute the work or the work must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Advances in Applied Mathematics.

Recommended Citation

Sills, Andrew, Doron Zeilberger. 2012. "Formulæ for the Number of Partitions of n into at Most m Parts (Using the Quazi-Polynomial Ansatz)." Advances in Applied Mathematics, 48 (5): 640-645. doi: 10.1016/j.aam.2011.12.003
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/180