  The thermodynamics of the anyon model projected on the lowest Landau level
(LLL) of an external magnetic field is addressed in the anti-screening regime,
where the flux tubes carried by the anyons are parallel to the magnetic field.
It is claimed that the LLL-anyon equation of state, which is known in the
screening regime, can be analytically continued in the statistical parameter
across the Fermi point to the antiscreening regime up to the vicinity (whose
width tends to zero when the magnetic field becomes infinite) of the Bose
point. There, an unphysical discontinuity arises due to the dropping of the
non-LLL eigenstates which join the LLL, making the LLL approximation no longer
valid. However, taking into account the effect of the non-LLL states at the
Bose point would only smoothen the discontinuity and not alter the physics
which is captured by the LLL projection: Close to the Bose point, the critical
filling factor either goes to infinity (usual bosons) in the screening
situation, or to 1/2 in the anti-screening situation, the difference between
the flux tubes orientation being relevant even when they carry an infinitesimal
fraction of the flux quantum. An exclusion statistics interpretation is
adduced, which explains this situation in semiclassical terms. It is further
shown how the exact solutions of the 3-anyon problem support this scenario as
far as the third cluster coefficient is concerned.
