where ∧ denotes the and bitwise operation, and I[k] is the kth bit of bitstring I, corresponding to the (k + 1)th spinorbital of determinant |I (remember that the orbital indices start at 1 and the bit indices start at 0). In other words, the ith bit of the phase mask is set to 1 if the number of electrons occupying the i + 1 lowest spinorbitals is odd, and 0 otherwise. When an electron of determinant |I is excited from orbital h to p, the associated phase factor is