12 citations · 76 across the 61 of their papers we have counts for
4 papers · 2 filters
A co-preLie structure from chronological loop erasure in graph walks
Loïc Foissy, Pierre-Louis Giscard, Cécile Mammez
We show that the chronological removal of cycles from a walk on a graph, known as Lawler's loop-erasing procedure, generates a preLie co-algebra on the vector space spanned by the…
Hopf algebraic structures on hypergraphs and multi-complexes
Loïc Foissy
Using the formalism of species and twisted objects, we introduce two structures of cointeracting bialgebras on hypergraphs, induced by two notions of induced sub-hypergraphs. We st…
Contractions and extractions on twisted bialgebras and coloured Fock functors
Loïc Foissy
We introduce a notion of extraction-contraction coproduct on twisted bialgebras, that is to say bialgebras in the category of linear species. If is a twisted bialgebra, a contr…
Hopf-algebraic structures on mixed graphs
Loïc Foissy
We introduce two coproducts on mixed graphs (that is to say graphs with both oriented and unoriented edges), the first one by separation of the vertices into two parts, and the sec…