  A semiclassical approach to the calculation of transport moments $M_m={\rm
Tr}[(t^\dag t)^m]$, where $t$ is the transmission matrix, was developed in [M.
Novaes, Europhys. Lett. 98, 20006 (2012)] for chaotic cavities with two leads
and broken time-reversal symmetry. The result is an expression for $M_m$ as a
perturbation series in 1/N, where N is the total number of open channels, which
is in agreement with random matrix theory predictions. The coefficients in this
series were related to two open combinatorial problems. Here we expand on this
work, including the solution to one of the combinatorial problems. As a
by-product, we also present a conjecture relating two kinds of factorizations
of permutations.
