12 citations · 76 across the 61 of their papers we have counts for
68 papers
Combinatorial twisted bialgebras and combinatorial twisted double bialgebras
Lo{ï}c Foissy
We provide in this text a new framework for a family of combinatorial Hopf algebras. We adopt for this the language of species and twisted bialgebras (also known as Hopf monoids).…
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…
Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
Loic Foissy, Xiao-Song Peng, Yunzhou Xie +1
In this paper, we first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We…
Construction of pre-and post-Lie algebras for stochastic PDEs
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…