Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line 
, with the coordinates of the upper left dot taken as (0,
0), are called conjugate (or transpose) partitions. For example, the conjugate partitions
illustrated above correspond to the partitions 
and 
of 15. A partition that is conjugate to itself is
said to be a self-conjugate partition.
The conjugate partition of a given partition 
is implemented in the Wolfram Function Repository as ResourceFunction["ConjugatePartition"][p].
