  Globular clusters display an anticorrelation between the fraction of the
first generation of stars ($N({\rm G1})/N({\rm tot})$) and the slope of the
present-day mass function of the clusters ($\alpha_{pd}$), which is
particularly significant for massive clusters. In the framework of the
binary-mediated collision scenario for the formation of the second-generation
stars in globular clusters, we test the effect of a varying stellar initial
mass function (IMF) of the G1 stars on the $(N({\rm G1})/N({\rm
tot}))-\alpha_{pd}$ anticorrelation. We use a simple collision model that has
only two input parameters, the shape of the IMF of G1 stars and the fraction of
G1 stars that coalesce to form second-generation stars. We show that a variable
efficiency of the collision process is necessary in order to explain the
$(N({\rm G1})/N({\rm tot}))-\alpha_{pd}$ anticorrelation; however, the scatter
in the anticorrelation can only be explained by variations in the IMF, and in
particular by variations in the slope in the mass interval $\approx$ (0.1-0.5)
M$_{\odot}$. Our results indicate that in order to explain the scatter in the
$(N({\rm G1})/N({\rm tot}))-\alpha_{pd}$ relation, it is necessary to invoke
variations in the slope in this mass range between $\approx -0.9$ and $\approx
-1.9$. Interpreted in terms of a Kroupa-like broken power law, this translates
into variations in the mean mass of between $\approx 0.2$ and $0.55$
M$_{\odot}$. This level of variation is consistent with what is observed for
young stellar clusters in the Milky Way and may reflect variations in the
physical conditions of the globular cluster progenitor clouds at the time the
G1 population formed or may indicate the occurrence of collisions between
protostellar embryos before stars settle on the main sequence.
