120 citations · 174 across the 19 of their papers we have counts for
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A forest formula for pre-Lie exponentials, Magnus' operator and cumulant-cumulant relations
Adrian Celestino, Frédéric Patras
Forest formulas that generalize Zimmermann's forest formula in quantum field theory have been obtained for the computation of the antipode in the dual of enveloping algebras of pre…
Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations
Kurusch Ebrahimi-Fard, Loïc Foissy, Joachim Kock +1
We establish and explore a relationship between two approaches to moment-cumulant relations in free probability theory: on one side the main approach, due to Speicher, given in ter…
Surjections and double posets
Frédéric Patras, Loïc Foissy
The theory and structure of the Hopf algebra of surjections (known as WQSym, the Hopf algebra of word quasi-symmetric functions) parallels largely the one of bijections (known as F…
Monotone, free, and boolean cumulants: a shuffle algebra approach
Kurusch Ebrahimi-Fard, Frederic Patras
The theory of cumulants is revisited in the "Rota way", that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinit…
Epsilon-noncrossing partitions and cumulants in free probability
Kurusch Ebrahimi-Fard, Frederic Patras, Roland Speicher
Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of -noncrossing partitions. It is shown that the set of such partitio…
A theory of pictures for quasi-posets
Loïc Foissy, Claudia Malvenuto, Frédéric Patras
The theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as Young diagrams and tableaux. Many r…