We introduce a new class of combinatorial objects, which we call ”bipieri tableaux”, which arise in a natural way from the evaluation of products consisting of (commutative or non-commutative) complete homogeneous symmetric functions and elementary symmetric functions in terms of Schur or Schur-like functions. Using signreversing involutions on bipieri tableaux, we prove an elegant coproduct formula for non-commutative Schur-hooks, and a new coproduct formula for elements of the shin basis indexed by a reverse hook composition. We show how bipieri tableaux maybe used to construct alternative combinatorial interpretations of special cases of the

classical Littlewood-Richardson rule.