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.
