Operators in second quantization

With \( N \) particles that can be distributed over \( n \) single-particle states, the total number of Slater determinats (and defining thereby the dimensionality of the system) is $$ \mathrm{dim}(\mathcal{H}) = \left(\begin{array}{c} n \\N\end{array}\right). $$ The total number of bit patterns is \( 2^n \).