Combinatorics and the thermodynamic limit for black holes in Loop Quantum Gravity

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combinatorial problems associated with the counting of black hole states in
loop quantum gravity can be analyzed by using suitable generating functions.
These not only provide very useful tools for exact computations, but can also
be used to perform an statistical analysis of the black hole degeneracy
spectrum, study the interesting substructure found in the entropy of
microscopic black holes and its asymptotic behavior for large horizon areas.
The methods that will be described are relevant for the discussion of the
thermodynamic limit for black holes in the area canonical ensemble. This is an
important issue in order to understand sub-leading corrections to the
Bekenstein-Hawking law.