Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y = - x, 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 6 + 3 + 3 + 2 + 1 and 5 + 4 + 3 + 1 + 1 + 1 of 15. A partition that is conjugate to itself is said to be a self-conjugate partition. The conjugate partition of a given partition p is implemented in the Wolfram Function Repository as ResourceFunction[ConjugatePartition][p].
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