we introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf… (More)

We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finite-dimensional, connected gradation. Dually, the vector… (More)

We describe a 2-parameters family of Hopf subalgebras of the non-commutative Connes-Kreimer Hopf algebra of planar rooted trees. They are organized into three isomorphism classes : a first one ,… (More)

We introduce an infinitesimal Hopf algebra of planar trees, generalising the construction of the non-commutative Connes-Kreimer Hopf algebra. A non-degenerate pairing and a dual basis are defined,… (More)

In [1, 3, 4, 5], a Hopf algebra of rooted trees HR was introduced. It was shown that the antipode of this algebra was the key of a problem of renormalization ([8]). HR is related to the Hopf algebra… (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and… (More)

We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an… (More)

We study the self-dual Hopf algebra HSP of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from HSP to the Hopf algebra of free quasi-symmetric functions FQSym… (More)

We describe four natural operad structures on the linear species of finite posets. The three last ones are set-theoretical and can be seen as a simplified version of the first, the same way the NAP… (More)

A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra… (More)