I'm using Macdonald's "Symmetric Functions and Hall Polynomials" as a reference and did not find what I was looking for -- apologies if I only missed it.
As an example, let us consider the partition $\lambda=(3,2,2,1)$ of $8$. Is the notation $2\lambda$ clear / in use / ... for describing the partition $(3,3,2,2,2,2,1,1)$ of $16$? (This actually corresponds to what Macdonald would write as $\lambda\cup\lambda$.)
If yes, do you have a reference? If no, what should I use?