Université Bourgogne Europe promotes international collaboration in discrete mathematics

Université Bourgogne Europe announces the publication of a scientific article resulting from a collaboration between José Luis Ramirez (Universidad Nacional de Colombia) and Jean Luc Baril (Laboratoire d’Informatique de Bourgogne – LIB). Submitted to arXiv in late 2025, this work is currently under review by the journal *Discrete Mathematics*.

This study focuses on counting paths within a geometric structure formed by a hexagonal stack of circles. The researchers are investigating how paths can form and connect within this environment, a problem linked to percolation theory, which studies the emergence of continuous connections in complex systems.

Using tools from algebraic combinatorics, they have developed methods for precisely calculating the number of possible paths according to defined movement rules.

An original result of this work is the interpretation of these paths as the movements of a ‘crawling caterpillar’. These trajectories are characterised by a parameter known as the kissing number, which corresponds to the number of circles located directly beneath the path, i.e. in contact with it. The researchers have established a generating function that allows these configurations to be counted based on this parameter.

Remarkably, these results coincide with the number of possible secondary structures for certain RNA molecules, thereby opening up new avenues of research at the interface between mathematics and biology.

This publication illustrates the dynamism of the international collaborations led by the University of Burgundy Europe and the interdisciplinary scope of fundamental mathematics.

To read the full article: https://arxiv.org/pdf/2511.13446