Séminaire Lotharingien de Combinatoire, 86B.82 (2022), 12 pp.
Nicolas Borie and Justine Falque
Product-Coproduct Prographs and Triangulations of the Sphere
Abstract.
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 product-coproduct 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.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
The following versions are available: