LetAn denote the number of objects of some type of \size"n ,a nd letCn denote the number of these objects which are connected. It is often the case that there is a relation between a generating function of the Cn’s and a generating function of theAn’s. Wright showed that if limn!1Cn=An = 1, then the radius of convergence of these generating functions must be zero. In this paper we prove that if the radius of convergence of the generating functions is zero, then lim sup n!1 Cn=An = 1, proving a conjecture of Compton; moreover, we show that lim infn!1Cn=An can assume any value between 0 and 1.
['Jason P. Bell']
When Structures Are Almost Surely Connected