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

2012; Elsevier BV; Volume: 48; Issue: 5 Linguagem: Inglês

10.1016/j.aam.2011.12.003

1090-2074

Andrew V. Sills, Doron Zeilberger,

Analytic Number Theory Research

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.