and the master index I counts the number of arrangements {j 1 , j 2 , . . . , j N } under the restriction that 1 ≤ j 1 < j 2 < . . . < j N ≤ 4K. I species the dimension of the many-body Hilbert space spanned by the basis of Slater determinants. Of course, q = 1, 2, . . . counts the excitation spectrum, with q = 1 corresponding to the ground state.