For the partition $(6,4,4,2)$ of integer $16$, if we draw its Young diagram with four rows of boxes, one below the other, of size $6$, $4$, $4$, and $2$, then flipping the resulting Young diagram along diagram gives another Young diagram, with row sizes $(4,4,3,3,1,1)$, and this partition of $16$ is called the conjugate partition of $(6,4,4,2)$.
Question. Is it possible to define or compute the conjugate of a partition, without looking it in terms of Young diagram?
In other words, to find, or define conjugate of a partition, is it necessary to represent it by Young diagram?