Computing Degeneracies of the Most Important Structures of Polycyclic Aromatic Hydrocarbons

We construct bijections between certain energetically favorable resonance-like structures in several classes of benzenoid compounds and some well-known combinatorial structures enumerated by Catalan and related numbers. In that way we derive explicit formulas for the number of such structures in the considered classes of compounds. We also list some open problems and indicate some possible directions for future research.