  Numerically solving a second quantised many-body model in the permutation
symmetric Fock space can be challenging for two reasons: (i) an increased
complication in the calculations of the matrix elements of various operators,
and (ii) a poor scaling of the cost of these calculations with the Fock space
size. We present a method that solves both these problems. We find a mapping
that can be used to simplify the calculations of the matrix elements. The
mapping is directly generated so its computational cost scales only linearly
with the space size and is negligible even for large enough sizes that approach
the thermodynamic limit.
