Hopf algebras in the free noncommutative cocommutative graded connected category exist with given dimension sequence iff the INVERTi transform is nonnegative.
Pattern groups and a poset based Hopf monoid.Journal of Combinatorial Theory, Series A, 172:105187
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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.