Systematic procedure for analyzing cumulants at any order

We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed to belong to different phase-space windows, which may overlap. It also allows for the analysis of cumulants at any order, using a simple algorithm rather than complicated expressions to be derived and coded by hand. In the case of azimuthal correlations, it automatically corrects to leading order for detector nonuniformity, and it is useful for numerous other applications as well. We discuss several of these applications: anisotropic flow, event-plane correlations, symmetric cumulants, and net baryon and net charge fluctuations.