where the ( i ) on the summation sign indicates that the sum is not over n i and is subject to the constraint that the total number of particles associated with the summation is N i = N − − n i . Note that Σ Σ ( i ) still depends on n i through the N i constraint, since in one case n i = 0 and Σ Σ ( i ) is evaluated with N i = N , while in the other case n i = 1 and Σ Σ ( i ) is evaluated with N i = N − − 1. To simplify the notation and to clearly indicate that Σ Σ ( i ) still depends on n i through N − − n i , define