Combinatorics of the SU(2) black hole entropy in loop quantum gravity

We use the combinatorial and number-theoretical methods developed in previous works by the authors to study black hole entropy in the new proposal put forth by Engle, Noui, and Pérez. Specifically, we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior, including the value of the Immirzi parameter and the coefficient of the logarithmic correction.The authors want to thank Alejandro Pérez for interesting discussions on this subject. The work was partially supported by the Spanish MICINN research grants FIS2008-01980, FIS2008-03221, FIS2008-06078-C03-02 and ESP2007-66542-C04-01, and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042). I.A. has been partially supported by RGI founds of the Center of Gravitation and Cosmology at the University of Wisconsin-Milwaukee