6 papers
The planar Hopf algebra of noncommutative multi-indices
Yong Yu, Xing Gao, Dominique Manchon
We construct the planar Linares--Otto--Tempelmayr Hopf algebra, thereby filling the missing planar noncommutative multi-index corner in the square relating the LOT, Butcher--Connes…
Extended generalized permutahedra, and cointeracting bialgebras
Gunnar Fløystad, Dominique Manchon
A Hopf monoid structure on extended generalized permutahedra (EGP) was recently introduced by M.Aguiar and F.Ardila. We investigate the existence of a cointeracting bialgebra struc…
Submodular functions, generalized permutahedra, conforming preorders, and cointeracting bialgebras
Gunnar Fløystad, Dominique Manchon
Submodular functions defined on the power set of a finite set are in bijection with generalized permutahedra $\egp(z)$. To any such we define a class of preorders, {\it con…
Controlled rough paths: a general Hopf-algebraic setting
Zhicheng Zhu, Xing Gao, Nannan Li +1
We set up controlled rough paths for a class of combinatorial Hopf algebras, encompassing shuffle, Butcher-Connes-Kreimer and Munthe-Kaas--Wright Hopf algebras. The class of contro…
Rough differential equations and planarly branched universal limit theorem
Xing Gao, Nannan Li, Dominique Manchon
The universal limit theorem is a central result in rough path theory, which has been proved for: (i) rough paths with roughness ; (ii) geometric ro…
Free Novikov algebras and the Hopf algebra of decorated multi-indices
Zhicheng Zhu, Xing Gao, Dominique Manchon
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the gr…