nontrivial. For the operators we consider in this article, this problem does not arise. As soon as a system of three or more gaint gravitons are considered, it will be necessary to deal with this issue. Fortunately a well defined approach to resolving these multiplicities has been outlined in [@Kimura:2008wy]. Basically, [@Kimura:2008wy] considers elements in the group algebra $CS_{n+m}$ which are invariant under conjugation by $CS_n\times CS_m$. The Cartan subalgebra of these elements are the natural generalization of the Jucys-Murphy elements which define a Cartan subalgebra for $S_n$[@Okunkov]. The multiplicities will be labelled by the eigenvalues of this Cartan subalgebra[@Kimura:2008wy]. It would be very interesting to work out the details of this proposal in the context of multigiant systems.

Given $R$ we imagine removing some boxes; after removing these boxes one is left with $r$. The removed boxes are assembled to produce $s$. If we specify both $R$ and the boxes that are to be removed to obtain $r$ we obtain every representation exactly once. For example, consider all possible operators that can be constructed from the following $R$ by removing the three boxes shown $$\young({\,}{\,},{\,}{\,},{\,}{*},{\,}{*},{\,},{\,},{\,},{*})$$ For the boxes that are removed, we must respect edges that are joined, which 