Rigorous results for branched polymer models with excluded volume

It is pointed out that on taking excluded volume into account for branched polymers there are modifications to previous work, such as that of Cayley and Polya on isomer enumeration. Indeed, it is argued that the classical Cayley–Polya count overestimates the corrected count by an arbitrarily large factor. Further, some limited rigorous results concerning the asymptotic behavior of isomer counts and of counts for polymer conformations are established.