  Quantum Geometry (the modern Loop Quantum Gravity using graphs and
spin-networks instead of the loops) provides microscopic degrees of freedom
that account for the black-hole entropy. However, the procedure for state
counting used in the literature contains an error and the number of the
relevant horizon states is underestimated. In our paper a correct method of
counting is presented. Our results lead to a revision of the literature of the
subject. It turns out that the contribution of spins greater then 1/2 to the
entropy is not negligible. Hence, the value of the Barbero-Immirzi parameter
involved in the spectra of all the geometric and physical operators in this
theory is different than previously derived. Also, the conjectured relation
between Quantum Geometry and the black hole quasi-normal modes should be
understood again.
