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

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 $p(n)$.
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