5 papers
Regularised double shuffle relations for planar Arborified Zeta Values
Pierre Catoire, Pierre J. Clavier, Ku-Yu Fan
We endow spaces of decorated planar rooted trees with new dendriform and tridendrifrom algebra structures and provide their combinatorial description. We then show that the planar…
Prediction with Missing Data: Target Probabilities and Missingness Mechanisms
Pierre Catoire, Robin Genuer, Cecile Proust-Lima
Conditions ensuring optimal parameter estimation in the presence of missing data are well established in inference, typically relying on the Missing-at-Random (MAR) assumption. In…
Effective approach of the tridendriform Schroeder tree algebra
Pierre Catoire, Jean Fromentin
We introduce a primitive computation problem in the free tridendriform algebra generated by one element which is a Hopf algebra based on Schroeder trees. We know a complex way to g…
Tridendriform and dendriform Zeta Values from Schroeder trees
Pierre Catoire, Pierre Clavier, Douglas Modesto da Fraga Candido
To build new generalisations of Multiple Zeta Values, we define new spaces of formal series and formal integrals. We show that they are tridendriform and dendriform algebras. This…
The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case
Pierre Catoire
We give the definition of left/right Post-Lie algebras and left/right Post-Hopf algebras and establish a link between those objects. We get a Cartier-Quillen-Milnor-Moore theorem f…