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math.RA2023
Hopf Algebra on Vincular Permutation Patterns
Joscha Diehl, Emanuele Verri
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specif…
math.RA2023
The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures
Marianne Clausel, Joscha Diehl, Raphael Mignot +3
We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step (over $\mathbb{R}^d…