Hopf algebras in the free noncommutative cocommutative graded connected category exist with given dimension sequence iff the INVERTi transform is nonnegative.
The primitives of the Hopf algebra of noncommutative symmetric functions.S˜ ao Paulo Journal of Mathematical Sciences, 1:175–202, dez
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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.