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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?

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I don't think the notation $2\lambda$ is clear as it could be taken to mean the partition $\lbrace 6,4,4,2 \rbrace$ of $16$. I would write $\lambda \cup \lambda, $ as Macdonald does. Sorry, I don't have any recommendation for a more succinct and unambiguous notation.

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