[@de; @Mello; @Koch:2007uv; @Bekker:2007ea] it was shown that operators which mix can differ at most by moving one box around on the Young diagram labeling the operator. Another interesting basis to consider is the Brauer basis[@Kimura:2007wy; @Kimura:2009wy]. This basis is built using Brauer algebra projectors. The structure constants of the Brauer algebra are $N$ dependent. There is an elegant construction of a class of BPS operators [@yusuke] in which the natural $N$ dependence appearing in the definition of the operator[@heslop] is reproduced by the Brauer algebra projectors[@yusuke]. Finally, another very natural approach to the problem, is to adopt a basis that has sharp quantum numbers for the global symmetries of the theory[@Brown:2007xh; @Brown:2008rr]. The action of the anomalous dimension operator in this sharp quantum number basis is very similar to the action in the restricted Schur basis: again operators which mix can differ at most by moving one box around on the Young diagram labeling the operator[@Brown:2008rs]. For further related interesting work see [@tomyusuke; @Huang:2010ne]. Finally, for a rather general approach which correctly counts and constructs the weak coupling BPS operators see[@jurgis].

We now conclude this introduction with a description of what is to follow. In section 2 we will 