Product-Coproduct Prographs and Triangulations of the Sphere

Prographes Produit-Coproduit et triangulations de la sphère

Nicolas Borie (1) , Justine Falque (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we explain how the classical Catalan families of objects involving paths, tableaux, triangulations, parentheses configurations and more generalize canonically to a three-dimensional version. In particular, we present productcoproduct prographs as central objects explaining the combinatorics of the triangulations of the sphere. Then we expose a natural way to extend the Tamari lattice to the product-coproduct prographs.

Mots clés: Tamari lattice Catalan numbers Prographs Triangulation Sphere; Tamari lattice; Catalan numbers; Prographs; Triangulation; Sphere

Domaines: Combinatoire [math.CO]

Nicolas Borie, Justine Falque. Product-Coproduct Prographs and Triangulations of the Sphere. FPSAC 2022, Jul 2022, Bengalore, India. ⟨hal-04346282⟩