Abstract
We introduce a family of multilinear operators on a quasi-shuffle algebra H, which we call Hoffman-Ihara operators. It generalizes the linear operators constructed by Hoffman and further studied by Hoffman and Ihara. We prove the formula on the composition of these operators, and show that this formula provides a unified and transparent understanding of some results on shuffle and quasi-shuffle products. An interpretation as an action of the operad of formal power series is also given.
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