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Evidence for an extraterrestrial flux of high-energy neutrinos has now beenfound in multiple searches with the IceCube detector. The first solid evidencewas provided by a search for neutrino events with deposited energies$\gtrsim30$ TeV and interaction vertices inside the instrumented volume. Recentanalyses suggest that the extraterrestrial flux extends to lower energies andis also visible with throughgoing, $\nu_\mu$-induced tracks from the Northernhemisphere. Here, we combine the results from six different IceCube searchesfor astrophysical neutrinos in a maximum-likelihood analysis. The combinedevent sample features high-statistics samples of shower-like and track-likeevents. The data are fit in up to three observables: energy, zenith angle andevent topology. Assuming the astrophysical neutrino flux to be isotropic and toconsist of equal flavors at Earth, the all-flavor spectrum with neutrinoenergies between 25 TeV and 2.8 PeV is well described by an unbroken power lawwith best-fit spectral index $-2.50\pm0.09$ and a flux at 100 TeV of$\left(6.7_{-1.2}^{+1.1}\right)\cdot10^{-18}\,\mathrm{GeV}^{-1}\mathrm{s}^{-1}\mathrm{sr}^{-1}\mathrm{cm}^{-2}$.Under the same assumptions, an unbroken power law with index $-2$ is disfavoredwith a significance of 3.8 $\sigma$ ($p=0.0066\%$) with respect to the bestfit. This significance is reduced to 2.1 $\sigma$ ($p=1.7\%$) if instead wecompare the best fit to a spectrum with index $-2$ that has an exponentialcut-off at high energies. Allowing the electron neutrino flux to deviate fromthe other two flavors, we find a $\nu_e$ fraction of $0.18\pm0.11$ at Earth.The sole production of electron neutrinos, which would be characteristic ofneutron-decay dominated sources, is rejected with a significance of 3.6$\sigma$ ($p=0.014\%$).

A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube