Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)

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.

Cited by in corpus (5)

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• A formula for the partition function that "counts"
• Coefficients of Sylvester's Denumerant
• Decomposition Methods for Nonlinear Optimization and Data Mining
• Some Families of Identities for Integer Partition Function