Cut-and-join operators and N = 4 super Yang-Mills

We show which multi-trace structures are compatible with the symmetrisation of local operators in N = 4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group SN.