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A New Lower Bound on the Number of Odd Values of the Ordinary Partition Function
Dennis Eichhorn
Department of Mathematics, University of California, Irvine, CA 92697, USA
deichhor@math.uci.edu
Annals of Combinatorics 13 (3) pp.297-303 September, 2009
AMS Subject Classification: 05A17, 11P81, 11P82
Abstract:
The parity of $p(n)$, the ordinary partition function, has been studied for at least a century, yet it still remains something of a mystery. Although much work has been done, the known lower bounds for the number of even and odd values of $p(n)$ for $n \leq N$ still appear to have a great deal of room for improvement. In this paper, we use classical methods to give a new lower bound for the number of odd values of $p(n)$.
Keywords: parity, partitions, odd values, p(n)

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