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

Andrew V. Sills; Doron Zeilberger

doi:10.1016/j.aam.2011.12.003

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

Andrew V. Sills, Doron Zeilberger

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 pm(n) for any desired m. We do this to demonstrate the power of "rigorous guessing" as facilitated by the quasi-polynomial ansatz.

Original language	American English
Journal	Advances in Applied Mathematics
Volume	48
DOIs	https://doi.org/10.1016/j.aam.2011.12.003
State	Published - May 1 2012

Keywords

Integer partitions

DC Disciplines

Education
Mathematics

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Cite this

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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 pm(n) for any desired m. We do this to demonstrate the power of {"}rigorous guessing{"} as facilitated by the quasi-polynomial ansatz.",

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AU - Zeilberger, Doron

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N2 - 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 pm(n) for any desired m. We do this to demonstrate the power of "rigorous guessing" as facilitated by the quasi-polynomial ansatz.

AB - 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 pm(n) for any desired m. We do this to demonstrate the power of "rigorous guessing" as facilitated by the quasi-polynomial ansatz.

KW - Integer partitions

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/180

U2 - 10.1016/j.aam.2011.12.003

DO - 10.1016/j.aam.2011.12.003

M3 - Article

SN - 0196-8858

VL - 48

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

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

Abstract

Keywords

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