Combinatorial Semigroup Bialgebras

preprint2013arXivOpen access

Abstract

This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the shuffle and stuffle algebras. We also consider the problem of constructing pairs of bases in duality and present Schützenberger's factorisations as an application.

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