Consider the following two partitions. Partition $\lambda=4^4=(4,4,4,4)$
o o o o
o o o o
o o o o
o o o o
And partition $\mu=(4,2,1,0)$
o o o o
o o
o
We can take the skew diagram of the two partitions $\lambda-\mu$ (or in other notation $\lambda /\mu$)
. . . .
. . o o
. o o o
o o o o
Now the question is, how do we read the resulting skew diagram in terms of partitions? Do we write
$$\lambda-\mu =(0,2,3,4)?$$
This does not seem right, since the elements of all partitions usually are ordered in decreasing order. Additionally, using such an object within a formula for construction of symmetric polynomials would lead to vanishing results if the partition is not ordered (see for example this paper). So the question remains: how exactly does one read a skew diagram as a partition? Thanks for any suggestion!
EDIT:
In the notation section of this paper the interpretation
$$(m^n-\mu)_i=m-\mu_{n+1-i}$$
is given, so that I guess in the above example we have $\lambda-\mu =(4,3,2,0)$. But that still does not tell us what to do when both $\lambda$ and $\mu$ have non-trivial shapes and i.e. $\lambda/\mu$ is a vertical strip.
A skew diagram is not a partition, so you cannot write it as a tuple. I would just write "$\lambda/\mu$ where $\lambda = 4444$ and $\mu = 421$." You need to keep both $\lambda$ and $\mu$ around to describe $\lambda/\mu$. Of course, if you're interested in some special situation you could make up your own notation.