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