Journal of the Ramanujan Mathematical Society

Volume 36, Issue 1, March 2021 pp. 33–37.

Nuclear partitions and a formula for p(n)

Authors: Robert Schneider
Author institution:Department of Mathematics, University of Georgia, Athens, Georgia 30602, U.S.A.

Summary: Define a “nuclear partition” to be an integer partition with no part equal to one. In this study we prove a simple formula to compute the partition function p(n) by counting only the nuclear partitions of n, a vanishingly small subset by comparison with all partitions of n as n → ∞. Variations on the proof yield other formulas for p(n), as well as Ramanujan-like congruences and an application to parity of the partition function.

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