What effect does Permanent Magnet have on an air-core coil?
The reactance of the coil will change and there are two opposing mechanisms at play: -


The permeability of the magnet will tend to increase inductance
The conductivity of the magnet will cause eddy currents that tend to decrease inductance


To what extent that either increases or decreases the coil's inductance is guesswork and will vary at different frequencies. I've seen situations where reactance/inductance doesn't change at all.

Another effect is that the eddy currents in the magnetic material will cause the magnet to take power from the AC circuit i.e. losses will increase.

At high frequencies the magnet will act like a plate of a capacitor and thus there will be a resonance effect. Again, without detail of the experiment this is hard to quantify.