Question

Fix natural numbers $n,m\in\mathbb{N}$. Given a partition $\lambda\vdash d$ with at most $n$ rows (and at most $m$ columns), we can define a partition $\lambda^\ast=(\lambda^\ast_1,\ldots,\lambda^\ast_n)$ by setting $\lambda^\ast_i:=m-\lambda_{n+1-i}$. Graphically, it is obtained by taking the complement of the Young diagram of $\lambda$ inside the $n\times m$ $-$ box $(m^n)$. Now, I'd be curious to learn about any combinatorial results involving this construction - but I don't know what it is called. If someone could tell me, that would be great - this way I'd not have such a hard time searching.

Answer 1

The "right" answer was given by Gjergji Zaimi in his comment above: Both "reverse partition" and "complementary partition" are terms that seem to be in use.