12 citations · 76 across the 61 of their papers we have counts for
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Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set . We study the needed structure o…
Typed angularly decorated planar rooted trees and generalized Rota-Baxter algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of parametrized Rota-Baxter algebras, which includes family and matching Rota-Baxter algebras. We study the structure needed on the set of paramet…
On extended associative semigroups
Loïc Foissy
We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutativ…
Generalized prelie and permutative algebras
Loïc Foissy
We study generalizations of pre-Lie algebras, where the free objects are based on rooted trees which edges are typed, instead of usual rooted trees, and with generalized pre-Lie pr…
Generalized associative algebras
Loïc Foissy
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup (generalization of matching or family ass…
From non-unitary wheeled PROPs to smooth amplitudes and generalised convolutions
Pierre J. Clavier, Loïc Foissy, Sylvie Paycha
We introduce the concept of TRAP (Traces and Permutations), which can roughly be viewed as a wheeled PROP (Products and Permutations) without unit. TRAPs are equipped with a horizo…