An operational calculus for the Mould operad

Frédéric Chapoton (1) , Florent Hivert (2) , Jean-Christophe Novelli (3) , Jean-Yves Thibon (3)

1 ICJ - Institut Camille Jordan
2 LIFAR - Laboratoire d'informatique fondamentale et appliquée de Rouen
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture of the first author about the inverse image of non-crossing trees in the dendriform operad. Finally, we explain a connection with the formalism of noncommutative symmetric functions.

Mots clés: Operads; Moulds; Trees; Noncommutative symmetric functions

Domaines: Algèbres quantiques [math.QA]; Combinatoire [math.CO]

Frédéric Chapoton, Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. An operational calculus for the Mould operad. International Mathematics Research Notices, 2008, 2008 (9), pp.1-22. ⟨10.1093/imrn/rnn018⟩. ⟨hal-00175958v3⟩