In this paper, we study different generalizations of the notion of
squarefreeness for ideals to the more general case of modules. We describe the
cones of Hilbert functions for squarefree modules in general and those
generated in degree zero. We give their extremal rays and defining
inequalities. For squarefree modules generated in degree zero, we compare the
defining inequalities of that cone with the classical Kruskal-Katona bound,
also asymptotically.Comment: 17 pages, 2 figures. This paper was produced during Pragmatic 201