Hopf algebras in the free noncommutative cocommutative graded connected category exist with given dimension sequence iff the INVERTi transform is nonnegative.
The characteristic polynomial of the Adams operators on graded connected Hopf algebras.Algebra & Number Theory, 9(3):547–583
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When are Hopf algebras determined by integer sequences?
Hopf algebras in the free noncommutative cocommutative graded connected category exist with given dimension sequence iff the INVERTi transform is nonnegative.