Year: 2025
Type: article
Abstract: . We introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the concept of mutually avoiding sets (which we rephrase as modules) and adapts in some sense the modular decomposition of graphs in the world of chirotopes. The associated tree always exists and is unique up to some appropriate constraints. We also show how to compute the number of triangulations of a chirotope efficiently, starting from its tree and the (weighted) numbers of triangulations of its parts.
DOI: 10.1137/24m1672201
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine, Institut Élie Cartan de Lorraine, Université Sorbonne Paris Nord, Laboratoire d'Informatique de Paris-Nord
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4392932935