  The calculation of the full counting statistics of the charge within a finite
interval of an interacting one-dimensional system of electrons is a
fundamental, yet as of now unresolved problem. Even in the non-interacting
case, charge counting turns out to be more difficult than anticipated because
it necessitates the calculation of a nontrivial determinant and requires
regularization. Moreover, interactions in a one-dimensional system are best
described using bosonization. However, this technique rests on a
long-wavelength approximation and is a priori inapplicable for charge counting
due to the sharp boundaries of the counting interval. To mitigate these
problems, we investigate the counting statistics using several complementary
approaches. To treat interactions, we develop a diagrammatic approach in the
fermionic basis, which makes it possible to obtain the cumulant generating
function up to arbitrary order in the interaction strength. Importantly, our
formalism preserves charge quantization in every perturbative order. We derive
an exact expression for the noise and analyze its interaction-dependent
logarithmic cutoff. We compare our fermionic formalism with the results
obtained by other methods, such as the Wigner crystal approach and numerical
calculations using the density-matrix renormalization group. Surprisingly, we
show good qualitative agreement with the Wigner crystal for weak interactions,
where the latter is in principle not expected to apply.
