Parity of number of partitions of an integer

[Richard Guy]

This is what is referred to?   R.

 2001a:11175 Eriksson, Nicholas $q$-series, elliptic curves, and odd 
values of the partition function.  Int. J. Math. Math. Sci.  22  (1999),  
no. 1, 55--65. 11P83 (11F20 11G05)

Summary: "Let $p(n)$ be the number of partitions of an integer $n$. Euler 
proved the following recurrence for $p(n)$: 
$$p(n)=\sum^\infty_{k=1}(-1)^{k+1}(p(n-\omega(k))+p(n-\omega(-k))),\tag{$*$}$$ 
where $\omega(k)=(3k^2+k)/2$. In view of Euler's result, one sees that it 
is fairly easy to compute $p(n)$ very quickly. However, many questions 
remain open even regarding the parity of $p(n)$. In this paper, we use 
various facts about elliptic curves and $q$-series to construct, for every 
$i\geq1$, finite sets $M_i$ for which $p(n)$ is odd for an odd number of 
$n\in M_i$."


On Thu, 4 Sep 2003, Hans Havermann wrote:

> benoit wrote:
> 
> > PARITY OF THE PARTITION FUNCTION
> > by KEN ONO
> 
> Ivars Peterson mentions Ken Ono's finding and Nicholas Eriksson's  
> subsequent extension:
> 
> http://www.maa.org/mathland/mathland_3_24.html
> 
> Eriksson's results are available as a PDF document:
> 
> http://ftp.fi.muni.cz/pub/muni.cz/EMIS/journals/IJMMS/volume-22/ 
> S0161171299220558.pdf?N=A
>