On some remarkable operads constructed from Baxter operators

Abstract

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this article is to study what type of (associative) algebras (and thus binary quadratic and non-symmetric operads) appear when such or such coalgebraic structures are used to decribe for instance combinatorial objects such as weighted directed graphs, trees, substitutions and so forth.