Abstract
We introduce a Combinatorial Hopf Algebra (CHA) with bases indexed by the partition diagrams indexing the bases for partition algebras. By analogy with the operation H α H β = H α · β for the complete homogeneous basis of the CHA NSym given by concatenating compositions α and β, we mimic this multiplication rule by setting H π H ρ = H π ⊗ ρ for partition diagrams π and ρ and for the horizontal concatenation π ⊗ ρ of π and ρ. This gives rise to a free, graded algebra ParSym , which we endow with a CHA structure.
Published Version
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