Formulæ for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz) |
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| Authors: | Andrew V. Sills Doron Zeilberger |
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| Affiliation: | 1. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30458-8093, USA;2. Department of Mathematics, Hill Center, Busch Campus, Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854-8019, USA |
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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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| Keywords: | 05A17 11P81 |
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