7 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…
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 rou…
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…
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…
A twisted Hopf algebra of finite topological quandles
Mohamed Ayadi, Dominique Manchon
This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind a…