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
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 277, 1979.Osima, M. "On the Irreducible Representations of the Symmetric Group." Canad. J. Math.4, 381-384, 1952.Watson, G. N. "Two Tables of Partitions." Proc. London Math. Soc.42, 550-556, 1936.
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). 
of 
is equal to the number of partitions of 
into distinct odd parts, and has generating function 
has generating function 
is a q-Pochhammer symbol. 