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Let R_n be the ring of coinvariants for the diagonal action of the symmetricgroup S_n. It is known that the character of R_n as a doubly-graded S_n modulecan be expressed using the Frobenius characteristic map as \nabla e_n, wheree_n is the n-th elementary symmetric function, and \nabla is an operator fromthe theory of Macdonald polynomials.  We conjecture a combinatorial formula for \nabla e_n and prove that it hasmany desirable properties which support our conjecture. In particular, we provethat our formula is a symmetric function (which is not obvious) and that it isSchur positive. These results make use of the theory of ribbon tableaugenerating functions of Lascoux, Leclerc and Thibon. We also show that avariety of earlier conjectures and theorems on \nabla e_n are special cases ofour conjecture.  Finally, we extend our conjectures on \nabla e_n and several of the resultssupporting them to higher powers \nabla^m e_n.

A combinatorial formula for the character of the diagonal coinvariants