Multi-electron coincidence spectroscopy: Triple Auger decay of Ar 2p and 2s holes

•A review of multi-electron coincidence experiments based on the use of magnetic bottle spectrometers is presented.•The Auger decay of Ar innershell holes by emission of three Auger electrons is studied.•The triple Auger decay of Ar 2p holes is a very weak path (0.2% of all Auger decays).•In the triple Auger decay of Ar 2p holes, Auger electrons are emitted simultaneously.•In the triple Auger decay of Ar 2s holes, Auger electrons are emitted in cascade.