Functions with optional argument named SquareFree :
bettiTablesWithHilbertFunction(...,SquareFree=>...) -- see bettiTablesWithHilbertFunction -- list or tally all Betti tables that can be obtained from monomial ideals with a particular (partial or complete) Hilbert function
monomialIdealsWithHilbertFunction(...,SquareFree=>...) -- see monomialIdealsWithHilbertFunction -- find all monomial ideals in a polynomial ring with a particular (partial or complete) Hilbert function