Species with grafting operators

par Yannic Vargas

jeudi 15 oct. 2026, 15:00 → 16:00 Europe/Paris

125 (Bat. Braconnier)

Inspired by the grafting operator of forests, we define grafting operators for combinatorial species. We show that these operators allow for the construction of up and down operators for species, which are combinatorial analogues of graded vector spaces with creation and annihilation operators. As an application, we reformulate the universal property of the Connes-Kreimer Hopf algebra of rooted forests within the framework of species with a grafting operator. Finally, we show how these operators allow for the construction of balanced pairs of up and down operators, appearing in quantum probability and perturbative algebraic quantum field theory. This is joint work with Pierre Clavier.