Packing problems (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Packing problems" in English language version.

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13doi.org

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mathscinet.ams.org

Stein, Sherman K. (March 1995), "Packing tripods", Mathematical entertainments, The Mathematical Intelligencer, 17 (2): 37–39, doi:10.1007/bf03024896, S2CID 124703268. Reprinted in Gale, David (1998), Gale, David (ed.), Tracking the Automatic ANT, Springer-Verlag, pp. 131–136, doi:10.1007/978-1-4612-2192-0, ISBN 0-387-98272-8, MR 1661863
Betke, Ulrich; Henk, Martin (2000). "Densest lattice packings of 3-polytopes". Computational Geometry. 16 (3): 157–186. arXiv:math/9909172. doi:10.1016/S0925-7721(00)00007-9. MR 1765181. S2CID 12118403.

arxiv.org

Donev, A.; Stillinger, F.; Chaikin, P.; Torquato, S. (2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. Bibcode:2004PhRvL..92y5506D. doi:10.1103/PhysRevLett.92.255506. PMID 15245027. S2CID 7982407.
Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. (2009). "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra". Nature. 462 (7274): 773–777. arXiv:1012.5138. Bibcode:2009Natur.462..773H. doi:10.1038/nature08641. PMID 20010683. S2CID 4412674.
Chen, E. R.; Engel, M.; Glotzer, S. C. (2010). "Dense Crystalline Dimer Packings of Regular Tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. Bibcode:2010arXiv1001.0586C. doi:10.1007/s00454-010-9273-0. S2CID 18523116.
Betke, Ulrich; Henk, Martin (2000). "Densest lattice packings of 3-polytopes". Computational Geometry. 16 (3): 157–186. arXiv:math/9909172. doi:10.1016/S0925-7721(00)00007-9. MR 1765181. S2CID 12118403.
Abrahamsen, Mikkel; Miltzow, Tillmann; Nadja, Seiferth (2020), Framework for $\exists \mathbb {R}$ -Completeness of Two-Dimensional Packing Problems, arXiv:2004.07558.

doi.org

Lodi, A.; Martello, S.; Monaci, M. (2002). "Two-dimensional packing problems: A survey". European Journal of Operational Research. 141 (2). Elsevier: 241–252. doi:10.1016/s0377-2217(02)00123-6.
Donev, A.; Stillinger, F.; Chaikin, P.; Torquato, S. (2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. Bibcode:2004PhRvL..92y5506D. doi:10.1103/PhysRevLett.92.255506. PMID 15245027. S2CID 7982407.
Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. (2009). "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra". Nature. 462 (7274): 773–777. arXiv:1012.5138. Bibcode:2009Natur.462..773H. doi:10.1038/nature08641. PMID 20010683. S2CID 4412674.
Chen, E. R.; Engel, M.; Glotzer, S. C. (2010). "Dense Crystalline Dimer Packings of Regular Tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. Bibcode:2010arXiv1001.0586C. doi:10.1007/s00454-010-9273-0. S2CID 18523116.
Stein, Sherman K. (March 1995), "Packing tripods", Mathematical entertainments, The Mathematical Intelligencer, 17 (2): 37–39, doi:10.1007/bf03024896, S2CID 124703268. Reprinted in Gale, David (1998), Gale, David (ed.), Tracking the Automatic ANT, Springer-Verlag, pp. 131–136, doi:10.1007/978-1-4612-2192-0, ISBN 0-387-98272-8, MR 1661863
Hudson, T. S.; Harrowell, P. (2011). "Structural searches using isopointal sets as generators: Densest packings for binary hard sphere mixtures". Journal of Physics: Condensed Matter. 23 (19): 194103. Bibcode:2011JPCM...23s4103H. doi:10.1088/0953-8984/23/19/194103. PMID 21525553. S2CID 25505460.
Smalley, I.J. (1963). "Simple regular sphere packings in three dimensions". Mathematics Magazine. 36 (5): 295–299. doi:10.2307/2688954. JSTOR 2688954.
Betke, Ulrich; Henk, Martin (2000). "Densest lattice packings of 3-polytopes". Computational Geometry. 16 (3): 157–186. arXiv:math/9909172. doi:10.1016/S0925-7721(00)00007-9. MR 1765181. S2CID 12118403.
Stoyan, Y. G.; Yaskov, G. N. (2010). "Packing identical spheres into a cylinder". International Transactions in Operational Research. 17: 51–70. doi:10.1111/j.1475-3995.2009.00733.x.
Teich, E.G.; van Anders, G.; Klotsa, D.; Dshemuchadse, J.; Glotzer, S.C. (2016). "Clusters of Polyhedra in Spherical Confinement". Proc. Natl. Acad. Sci. U.S.A. 113 (6): E669–E678. Bibcode:2016PNAS..113E.669T. doi:10.1073/pnas.1524875113. PMC 4760782. PMID 26811458.
Melissen, J. (1995). "Packing 16, 17 or 18 circles in an equilateral triangle". Discrete Mathematics. 145 (1–3): 333–342. doi:10.1016/0012-365X(95)90139-C.
Klarner, D.A.; Hautus, M.L.J (1971). "Uniformly coloured stained glass windows". Proceedings of the London Mathematical Society. 3. 23 (4): 613–628. doi:10.1112/plms/s3-23.4.613.

eoearth.org

C.Michael Hogan. 2010. Abiotic factor. Encyclopedia of Earth. eds Emily Monosson and C. Cleveland. National Council for Science and the Environment. Washington DC

harvard.edu

ui.adsabs.harvard.edu

Donev, A.; Stillinger, F.; Chaikin, P.; Torquato, S. (2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. Bibcode:2004PhRvL..92y5506D. doi:10.1103/PhysRevLett.92.255506. PMID 15245027. S2CID 7982407.
Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. (2009). "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra". Nature. 462 (7274): 773–777. arXiv:1012.5138. Bibcode:2009Natur.462..773H. doi:10.1038/nature08641. PMID 20010683. S2CID 4412674.
Chen, E. R.; Engel, M.; Glotzer, S. C. (2010). "Dense Crystalline Dimer Packings of Regular Tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. Bibcode:2010arXiv1001.0586C. doi:10.1007/s00454-010-9273-0. S2CID 18523116.
Hudson, T. S.; Harrowell, P. (2011). "Structural searches using isopointal sets as generators: Densest packings for binary hard sphere mixtures". Journal of Physics: Condensed Matter. 23 (19): 194103. Bibcode:2011JPCM...23s4103H. doi:10.1088/0953-8984/23/19/194103. PMID 21525553. S2CID 25505460.
Teich, E.G.; van Anders, G.; Klotsa, D.; Dshemuchadse, J.; Glotzer, S.C. (2016). "Clusters of Polyhedra in Spherical Confinement". Proc. Natl. Acad. Sci. U.S.A. 113 (6): E669–E678. Bibcode:2016PNAS..113E.669T. doi:10.1073/pnas.1524875113. PMC 4760782. PMID 26811458.

jstor.org

Smalley, I.J. (1963). "Simple regular sphere packings in three dimensions". Mathematics Magazine. 36 (5): 295–299. doi:10.2307/2688954. JSTOR 2688954.

nih.gov

pubmed.ncbi.nlm.nih.gov

Donev, A.; Stillinger, F.; Chaikin, P.; Torquato, S. (2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. Bibcode:2004PhRvL..92y5506D. doi:10.1103/PhysRevLett.92.255506. PMID 15245027. S2CID 7982407.
Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. (2009). "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra". Nature. 462 (7274): 773–777. arXiv:1012.5138. Bibcode:2009Natur.462..773H. doi:10.1038/nature08641. PMID 20010683. S2CID 4412674.
Hudson, T. S.; Harrowell, P. (2011). "Structural searches using isopointal sets as generators: Densest packings for binary hard sphere mixtures". Journal of Physics: Condensed Matter. 23 (19): 194103. Bibcode:2011JPCM...23s4103H. doi:10.1088/0953-8984/23/19/194103. PMID 21525553. S2CID 25505460.
Teich, E.G.; van Anders, G.; Klotsa, D.; Dshemuchadse, J.; Glotzer, S.C. (2016). "Clusters of Polyhedra in Spherical Confinement". Proc. Natl. Acad. Sci. U.S.A. 113 (6): E669–E678. Bibcode:2016PNAS..113E.669T. doi:10.1073/pnas.1524875113. PMC 4760782. PMID 26811458.

ncbi.nlm.nih.gov

Teich, E.G.; van Anders, G.; Klotsa, D.; Dshemuchadse, J.; Glotzer, S.C. (2016). "Clusters of Polyhedra in Spherical Confinement". Proc. Natl. Acad. Sci. U.S.A. 113 (6): E669–E678. Bibcode:2016PNAS..113E.669T. doi:10.1073/pnas.1524875113. PMC 4760782. PMID 26811458.

semanticscholar.org

api.semanticscholar.org

Donev, A.; Stillinger, F.; Chaikin, P.; Torquato, S. (2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. Bibcode:2004PhRvL..92y5506D. doi:10.1103/PhysRevLett.92.255506. PMID 15245027. S2CID 7982407.
Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. (2009). "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra". Nature. 462 (7274): 773–777. arXiv:1012.5138. Bibcode:2009Natur.462..773H. doi:10.1038/nature08641. PMID 20010683. S2CID 4412674.
Chen, E. R.; Engel, M.; Glotzer, S. C. (2010). "Dense Crystalline Dimer Packings of Regular Tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. Bibcode:2010arXiv1001.0586C. doi:10.1007/s00454-010-9273-0. S2CID 18523116.
Stein, Sherman K. (March 1995), "Packing tripods", Mathematical entertainments, The Mathematical Intelligencer, 17 (2): 37–39, doi:10.1007/bf03024896, S2CID 124703268. Reprinted in Gale, David (1998), Gale, David (ed.), Tracking the Automatic ANT, Springer-Verlag, pp. 131–136, doi:10.1007/978-1-4612-2192-0, ISBN 0-387-98272-8, MR 1661863
Hudson, T. S.; Harrowell, P. (2011). "Structural searches using isopointal sets as generators: Densest packings for binary hard sphere mixtures". Journal of Physics: Condensed Matter. 23 (19): 194103. Bibcode:2011JPCM...23s4103H. doi:10.1088/0953-8984/23/19/194103. PMID 21525553. S2CID 25505460.
Betke, Ulrich; Henk, Martin (2000). "Densest lattice packings of 3-polytopes". Computational Geometry. 16 (3): 157–186. arXiv:math/9909172. doi:10.1016/S0925-7721(00)00007-9. MR 1765181. S2CID 12118403.

utwente.nl

research.utwente.nl

Melissen, J. (1995). "Packing 16, 17 or 18 circles in an equilateral triangle". Discrete Mathematics. 145 (1–3): 333–342. doi:10.1016/0012-365X(95)90139-C.

wolfram.com

mathworld.wolfram.com

"Circle Packing".

worldcat.org

Torquato, S.; Jiao, Y. (August 2009). "Dense packings of the Platonic and Archimedean solids". Nature. 460 (7257): 876–879. arXiv:0908.4107. Bibcode:2009Natur.460..876T. doi:10.1038/nature08239. ISSN 0028-0836. PMID 19675649. S2CID 52819935.