15h15: Feynman-like combinatorial diagrams and the EGF Hadamard Product By G.H.E.Duchamp (LIPN, Université Paris XIII)

Abstract. We consider two aspects of the product formula for formal power series applied to combinatorial field theories. Firstly, we remark that the case when the functions involved in the product formula are free exponentials (like in the derivation of Bell polynomials) is of special interest as it leads to groups of substitutions and a correspondence with vector fields on the line. Secondly, we discuss deformations (counting natural graph parameters as crossings and superpositions) of the Feynman-like algebra arising from the product formula of two free exponentials. This results in a true Hopf deformation of this algebra.