14 citations · 58 across the 23 of their papers we have counts for
5 papers · 1 filter
Graftings and cograftings for species
Pierre Clavier, Yannic Vargas
We introduce graftings and cograftings for vector species, modelled on the elementary operations of adjoining and deleting a root in a rooted forest. We relate these maps to operad…
Tridendriform and dendriform Zeta Values from Schroeder trees
Pierre Catoire, Pierre Clavier, Douglas Modesto da Fraga Candido
To build new generalisations of Multiple Zeta Values, we define new spaces of formal series and formal integrals. We show that they are tridendriform and dendriform algebras. This…
Coalgebras, bialgebras and Rota-Baxter algebras from shuffles of rooted forests
Pierre J. Clavier, Douglas Modesto
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with the…
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…
ProPs of graphs and generalised traces
Pierre J. Clavier, Loic Foissy, Sylvie Paycha
We assign generalised convolutions (resp. traces) to graphs whose edges are decorated by smooth kernels (resp. smoothing operators) on a closed manifold. To do so, we introduce the…