  The genuine event-by-event correlations between three flow amplitudes are
measured for the first time in Pb-Pb collisions at $\sqrt{s_{\rm {NN}}} = 2.76$
TeV by the ALICE Collaboration at the Large Hadron Collider. The results are
obtained with recently developed observables, the higher order Symmetric
Cumulants (SC), in the midrapidity region $|\eta| < 0.8$ and the transverse
momentum range $0.2 < p_{\mathrm T} < 5.0$ GeV/$c$. These higher order
observables show the same robustness against systematic biases arising from
nonflow effects as the two-harmonic SC. The new results cannot be interpreted
in terms of lower order flow measurements, since they are dominated by
different patterns of event-by-event flow fluctuations. The results are
compared with expectations from initial state models such as T$_{\rm{R}}$ENTo
and next-to-leading order perturbative-QCD+saturation model of initial
conditions, followed by iEBE-VISHNU and EKRT viscous hydrodynamic calculations.
Model comparisons provide an indication of the development of genuine
correlations between the elliptic $v_2$, the triangular $v_3$ and the
quadrangular $v_4$ flow amplitudes during the collective evolution of the
medium. The comparison with the predictions for the correlations between $v_2$,
$v_3$ and the pentagonal flow magnitude $v_5$ illustrate the need for further
tuning of model parameterizations. Therefore, these results can provide new and
independent constraints for the initial conditions and system properties of
nuclear matter created in heavy-ion collisions, complementary to previous flow
measurements.
