Detailed black hole state counting in loop quantum gravity

The combinatorial problems associated with the counting of black hole states in loop quantum gravity can be analyzed by using suitable generating functions. These can be used to perform a statistical analysis of the black hole degeneracy spectrum, study the interesting sub-structure found in the entropy of microscopic black holes, and its asymptotic behaviour for large horizon areas. They are also relevant for the discussion of the thermodynamic limit for black holes, and the understanding of sub-leading corrections to the Bekenstein-Hawking law