[seqfan] need some help with partitions (cores and quotients)

[Wouter Meeussen]

hi All,

can anybody help me understand how to recombine the p-core and p-quotients of a partition to get the original partition back?

Say that I decompose {5, 3, 2, 1, 1, 1} into core {2, 1, 1} and quotients {}, {1}, {1, 1}
then there is a way to inverse that operation.
I’ve been looking at all the literature that I can find on the web, but to no avail.

It seems to be so selfevident that no-one cares to explain. R.P. Stanley even puts the whole p-core p-quotient item in an exercise!  
and van Leeuwen, who usually has a sublime didactic style (see  http://www-math.univ-poitiers.fr/~maavl/pdf/edgeseqs.pdf ) lets me down.

(See also http://arxiv.org/pdf/1008.4205v1.pdf )

Any high school teachers spare a minute?

[I’d like to program it in Mathematica and experiment with it]
[Got the decomposition operation working nicely                   ]

Wouter.