Optimal packings of two to four equal circles on any flat torus

DOI10.1016/j.disc.2019.111597zbMath1442.52014arXiv1708.05395OpenAlexW2965242053WikidataQ127399181 ScholiaQ127399181MaRDI QIDQ2329183

Jennifer Kenkel, Hanson Smith, Madeline Brandt, AnnaVictoria Ellsworth, William C. Dickinson

Publication date: 17 October 2019

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05395

zbMATH Keywords

flat torusequal circle packingrigidity theorypacking graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Circle packings and discrete conformal geometry (52C26)

Related Items (2)

Unnamed Item ⋮ Optimal packings of 2,3, and 4 equal balls into a cubical flat 3-torus

Uses Software

• Mathematica
• nauty
• Traces
• Groups & Graphs

Cites Work

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• Optimal packings of up to six equal circles on a triangular flat torus
• A linear programming algorithm to test for jamming in hard-sphere packings
• Optimal packings of up to five equal circles on a square flat torus
• Packing disks on a torus
• Patterns and structures in disk packings
• Practical graph isomorphism. II.
• Producing dense packings of cubes
• Densest Packings of Congruent Circles in an Equilateral Triangle
• Graphs, Algorithms, and Optimization
• The Densest Packing of 9 Circles in a Square
• On 2D packings of cubes in the torus
• Compact Riemann surfaces. An introduction to contemporary mathematics
• Densest circle packing on the flat torus
• Optimal packings of congruent circles on a square flat torus

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