2019/12/02 by Schneider, Robert
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1912.00575
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.