Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stanley's Partition Function   Stanley defined a partition function t(n) as the number of partitions
$\lambda$ of n such that the number of odd parts of $\lambda$ is congruent to
the number of odd parts of the conjugate partition $\lambda'$ modulo 4. We show
that t(n) equals the number of partitions of n with an even number of hooks of
even length. We derive a closed-form formula for the generating function for
the numbers p(n)-t(n). As a consequence, we see that t(n) has the same parity
as the ordinary partition function p(n) for any n. A simple combinatorial
explanation of this fact is also provided.

34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio