The conjpart(p) command computes and returns the conjugate partition of p.

A partition  of a positive integer  may be represented visually by its Ferrer's diagram. This is a diagram composed of dots in rows, in which the th row consists of  dots, for . The total number of dots in the diagram is equal to the number . For example, the partition  of  has the Ferrer's diagram:

consisting of ten dots arranged in three rows, with two dots in the first row, three dots in the second, and five dots in the third row.

Two partitions (of a positive integer ) are said to be conjugates if their Ferrer's diagrams are conjugate, which means that one is obtained from the other, by reflection along the anti-diagonal, by writing the rows as columns and columns as rows. For example, the conjugate of the Ferror diagram above is:

which represents the partition . Therefore, the partitions  and  are conjugate partitions.