6 citations · 9 across the 5 of their papers we have counts for
5 papers
The Universal Post-Lie-Rinehart Algebra of Planar Aromatic Trees
Ludwig Rahm
This paper defines the algebraic structure of tracial post-Lie-Rinehart algebras and describes the free object in this category. Post-Lie-Rinehart algebras is a generalisation of p…
A Survey on the Munthe-Kaas-Wright Hopf Algebra
Kurusch Ebrahimi-Fard, Ludwig Rahm
We survey the Munthe-Kaas--Wright Hopf algebra defined on planar rooted trees. This algebra serves a role akin to that of the Butcher--Connes--Kreimer Hopf algebra on non-planar ro…
Planar Regularity Structures
Ludwig Rahm
Branched rough paths, used to solve ODEs on , have been generalised in two different directions. In one direction, there are regularity structures aimed at solving SPDE…
Translations of rough paths in combinatorial Hopf algebras
Ludwig Rahm
We generalize Bruned et.al.'s notion of translation in geometric and branched rough paths to a notion of translation in rough paths over any combinatorial Hopf algebra. We show tha…
An operadic approach to substitution in Lie-Butcher series
Ludwig Rahm
The paper follows an operadic approach to provide a bialgebraic description of substitution for Lie-Butcher series. We first show how the well-known bialgebraic description for sub…