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05/28/2023
Shield tilings
We provide a complete description of the edge-to-edge tilings with a reg...
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05/22/2023
Packing unequal disks in the Euclidean plane
A packing of disks in the plane is a set of disks with disjoint interior...
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11/15/2022
Geometrical Penrose Tilings have Finite Type
Rhombus Penrose tilings are tilings of the plane by two decorated rhombi...
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11/05/2022
Density of triangulated ternary disc packings
We consider ternary disc packings of the plane, i.e. the packings using ...
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05/27/2022
A General approach to Ammann bars for aperiodic tilings
Ammann bars are formed by segments (decorations) on the tiles of a tilin...
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01/03/2022
Purely local growth of a quasicrystal
Self-assembly is the process in which the components of a system, whethe...
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07/29/2021
Density of Binary Disc Packings:Lower and Upper Bounds
We provide, for any r∈ (0,1), lower and upper bounds on the maximal dens...
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04/26/2021
Compact Packings are not always the Densest
We provide a counterexample to a conjecture by B. Connelly about density...
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06/25/2020
Density of Binary Disc Packings: Playing with Stoichiometry
We consider the packings in the plane of discs of radius 1 and √(2)-1 wh...
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02/17/2020
Density of Binary Compact Disc Packings
A disc packing in the plane is compact if its contact graph is a triangu...
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12/04/2019
A Densest ternary circle packing in the plane
We consider circle packings in the plane with circles of sizes 1, r≃ 0.8...
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12/04/2019
Compact packings of space with three sizes of spheres
A sphere packing of the three-dimensional Euclidean space is compact if ...
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12/17/2018
Canonical projection tilings defined by patterns
We give a necessary and sufficient condition on a d-dimensional affine s...
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08/31/2018
Empilements compacts avec trois tailles de disque
Discs form a compact packing of the plane if they are interior disjoint ...
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08/31/2018
Compact packings of the plane with three sizes of discs
Discs form a compact packing of the plane if they are interior disjoint ...
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11/09/2017