English

Product-Coproduct Prographs and Triangulations of the Sphere

Combinatorics 2022-02-14 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.2202.05757,
  title  = {Product-Coproduct Prographs and Triangulations of the Sphere},
  author = {Nicolas Borie and Justine Falque},
  journal= {arXiv preprint arXiv:2202.05757},
  year   = {2022}
}