QCD jet rates with the inclusive generalized k(t) algorithms

We derive generating functions, valid to next-to-double logarithmic accuracy, for QCD jet rates according to the inclusive forms of the k(t), Cambridge/Aachen and anti-k(t) algorithms, which are equivalent at this level of accuracy. We compare the analytical results with jet rates and average jet multiplicities from the SHERPA event generator, and study the transition between Poisson-like and staircase-like behaviour of jet ratios.