A self-conjugate partition is a partition whose conjugate partition is equivalent to itself.
The Ferrers diagrams corresponding to the self-conjugate
partitions for 
are illustrated above. The numbers of self-conjugate partitions of 
, 2, ... are 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4,
5, 5, 5, 6, 7, ... (OEIS A000700).
The number of self-conjugate partitions 
of 
is equal to the number of partitions of 
into distinct odd parts, and has generating
function
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
and 
has generating function
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
where 
is a q-Pochhammer symbol.
