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math.RA2009★ 4 cited
Systems of Dyson-Schwinger equations
Loïc Foissy
We consider systems of combinatorial Dyson-Schwinger equations (briefly, SDSE) X_1=B^+_1(F_1(X_1,...,X_N))...X_N=B^+_N(F_N(X_1,...,X_N)) in the Connes-Kreimer Hopf algebra H_I of r…
math.RA2009
The operads of planar forests are Koszul
Loïc Foissy
We describe the Koszul dual of two quadratic operads on planar forests introduced to study the infinitesimal Hopf algebra of planar rooted trees and prove that these operads are Ko…
math.RA2009
The infinitesimal Hopf algebra and the operads of planar forests
Loïc Foissy
We introduce two operads which own the set of planar forests as a basis. With its usual product and two other products defined by different types of graftings, the algebra of plana…