10 papers · 1 filter
Bialgebraic structures on boolean functions
Loïc Foissy
We study several bialgebraic structures on boolean functions, that is to say maps defined on the set of subsets of a finite set , taking the value on . Examples o…
Operads and bialgebras of multi-indices, and Novikov algebras
Loïc Foissy
Noncommutative multi-indices are noncommutative monomials in a -indexed family of indeterminates. We define on them a -graded operadic structure, with the h…
Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
Loïc Foissy, Yunzhou Xie, Dawei Zhang +1
The concept of weighted infinitesimal bialgebras provides an algebraic framework for understanding the non-homogeneous associative Yang-Baxter equation. In this paper, we endow the…
Noncrossing arithmetic
Kurusch Ebrahimi-Fard, Loïc Foissy, Joachim Kock +1
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory…
Construction of pre-and post-Lie algebras for stochastic PDEs
Loïc Foissy, Loïc Foissy
We give and study a construction of pre-Lie algebra structures on rooted trees whose edges and vertices are decorated, with a grafting product acting, through a map , both on th…
Cointeraction on noncrossing partitions and related polynomial invariants
Loïc Foissy
We study the structure of two cointeracting bialgebras on noncrossing partitions appearing in the theory of free probability. The first coproduct is given by separation of the bloc…