# GALaC team at LRI, Paris-Sud

GALaC is a research group at LRI, Paris-Sud University. We are focused on graph theory, combinatorics and network distributed systems algorithmic.

A global presentation of research activities in GALaC was made in 2013 for the AERES evaluation: Slides AERES 2013 and projet.

## Recent Posts

## Realizing Geometrically s-Permutahedra via Flow Polytopes

summary: In 2020, Ceballos and Pons defined s-decreasing trees with s being a weak composition. They described an order on these objects called the s-weak order which gives them the order structure of a lattice. They further conjectured that this structure could be realized geometrically as the 1-skeleton of a ...

## Density of sphere packings: from coins to oranges

summary: How to stack an infinite number of oranges to maximize the proportion of the covered space? Kepler conjectured that the "cannonball" packing is an optimal way to do it. This conjecture took almost 400 years to prove and the proof of Hales and Ferguson consists of 6 papers and ...

## A realization of poset associahedra as sections of graph associahedra

Poset associahedra are a family of convex polytopes introduced by Pavel Galashin in 2021, each one associated to a partially ordered set, that generalize the classical associahedron. Galashin describes the combinatorial structure of poset associahedra, and he realizes them as convex polytopes. However, his construction is not completely satisfactory. In ...

Translations: fr