23 citations · 120 across the 28 of their papers we have counts for
6 papers · 1 filter
On Dense Tetrahedra in Binary Sphere Packings
Thomas Fernique, Daria Pchelina
This paper considers the density of tetrahedra arising in a specific decomposition of packings of unequal spheres in . It aims to extend a bound obtained in 2D in the…
Packing unequal disks in the Euclidean plane
Thomas Fernique
A packing of disks in the plane is a set of disks with disjoint interiors. This paper is a survey of some open questions about such packings. It is organized into five themes: comp…
Density of binary disc packings: lower and upper bounds
Thomas Fernique
We provide, for any , lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius and . The lower bounds are mostly folk…
Compact Packings are not always the Densest
Thomas Fernique, Daria Pchelina
We provide a counterexample to a conjecture by B. Connelly about density of circle packings
Compact packings of space with three sizes of spheres
Thomas Fernique
A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distanc…
Compact packings of the space with two sizes of spheres
Thomas Fernique
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean s…