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We have investigated resonant tunneling experiments through a quantum antidot in the quantum Hall regime. When the two edge states with different spins of the lowest Landau level are localized around an antidot conductance exhibits the paired $h/2e$ Aharonov-Bohm oscillations. Using a tilted magnetic field technique we observed evolution of the oscillation with the Zeeman energy. A concomitant change is observed in the conduction spectra at finite source-drain bias. These results are interpreted by the energy spacings between the single particle states with the same spin and the Zeeman splitting.

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