참고문헌 (21)

1. Phys. Rev. E A Andreanov 86 041117 2012 10.1103/PhysRevE.86.041117 Andreanov, A., Scardicchio, A.: Random perfect lattices and the sphere packing problem. Phys. Rev. E 86, 041117 (2012) 

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2. J. Stat. Mech. Theory Exp. A Andreanov 2016 11 113301 2016 10.1088/1742-5468/2016/11/113301 Andreanov, A., Scardicchio, A., Torquato, S.: Extreme lattices: symmetries and decorrelation. J. Stat. Mech. Theory Exp. 2016(11), 113301 (2016) 

   상세보기

3. D Avis 177 2000 DMV Seminar Polytopes-Combinatorics and Computation 10.1007/978-3-0348-8438-9_9 Avis, D.: A revised implementation of the reverse search vertex enumeration algorithm. In: Kalai, G., Ziegler, G. (eds.) Polytopes-Combinatorics and Computation. DMV Seminar, vol. 29, pp. 177-198. Birkhäuser, Basel (2000) 

   

4. MS Bazaraa 2006 Nonlinear Programming 3 10.1002/0471787779 Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, 3rd edn. Wiley, Hoboken (2006) 

   

5. Nat. Comm. P Charbonneau 5 3725 2014 10.1038/ncomms4725 Charbonneau, P., Kurchan, J., Parisi, G., Urbani, P., Zamponi, F.: Fractal free energy landscapes in structural glasses. Nat. Comm. 5, 3725 (2014) 

   상세보기

6. Notices Am. Math. Soc. H Cohn 64 2 102 2017 10.1090/noti1474 Cohn, H.: A conceptual breakthrough in sphere packing. Notices Am. Math. Soc. 64(2), 102-115 (2017) 

   상세보기

7. Ann. Math. H Cohn 185 3 1017 2017 10.4007/annals.2017.185.3.8 Cohn, H., Kumar, A., Miller, S.D., Radchenko, D., Viazovska, M.: The sphere packing problem in dimension 24. Ann. Math. 185(3), 1017-1033 (2017) 

   상세보기

8. JH Conway 1999 Grundlehren der Mathematischen Wissenschaften Sphere Packings, Lattices, and Groups 3 10.1007/978-1-4757-6568-7 Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups. Grundlehren der Mathematischen Wissenschaften, vol. 290, 3rd edn. Springer, New York (1999) 

   

9. Math. Z. L Fejes Tóth 46 83 1940 10.1007/BF01181430 Fejes Tóth, L.: Über einen geometrischen Satz. Math. Z. 46, 83-85 (1940) 

   상세보기

10. Ann. Math. TC Hales 162 3 1065 2005 10.4007/annals.2005.162.1065 Hales, T.C.: A proof of the Kepler conjecture. Ann. Math. 162(3), 1065-1185 (2005) 

    상세보기

11. Phys. Rev. E Y Kallus 87 063307 2013 10.1103/PhysRevE.87.063307 Kallus, Y.: Statistical mechanics of the lattice sphere packing problem. Phys. Rev. E 87, 063307 (2013) 

    상세보기

12. Phys. Rev. E Y Kallus 88 062151 2013 10.1103/PhysRevE.88.062151 Kallus, Y., Marcotte, E., Torquato, S.: Jammed lattice sphere packings. Phys. Rev. E 88, 062151 (2013) 

    상세보기

13. Phys. Rev. E E Marcotte 87 063303 2013 10.1103/PhysRevE.87.063303 Marcotte, E., Torquato, S.: Efficient linear programming algorithm to generate the densest lattice sphere packings. Phys. Rev. E 87, 063303 (2013) 

    상세보기

14. SIAM J. Comput. D Micciancio 42 3 1364 2010 10.1137/100811970 Micciancio, D., Voulgaris, P.: A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations. SIAM J. Comput. 42(3), 1364-1391 (2010) 

    상세보기

15. Dokl. Akad. Nauk SSSR SS Ryshkov 194 514 1970 Ryshkov, S.S.: The polyhedron $$\mu (m)$$ and certain extremal problems of the geometry of numbers. Dokl. Akad. Nauk SSSR 194, 514-517 (1970). (in Russian) 

16. A Schürmann 2009 University Lecture Series Computational Geometry of Positive Definite Quadratic Forms: Polyhedral Reduction Theories, Algorithms, and Applications Schürmann, A.: Computational Geometry of Positive Definite Quadratic Forms: Polyhedral Reduction Theories, Algorithms, and Applications. University Lecture Series, vol. 48. American Mathematical Society, Providence (2009) 

17. Adv. Math. A Schürmann 225 5 2546 2010 10.1016/j.aim.2010.05.002 Schürmann, A.: Perfect, strongly eutactic lattices are periodic extreme. Adv. Math. 225(5), 2546-2564 (2010) 

    상세보기

18. A Schürmann 185 2013 Contemporary Mathematics Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms 10.1090/conm/587/11686 Schürmann, A.: Strict periodic extreme lattices. In: Chan, W.K., et al. (eds.) Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. Contemporary Mathematics, vol. 587, pp. 185-190. American Mathematical Society, Providence (2013) 

    

19. Electron. Res. Announc. Amer. Math. Soc MD Sikirić 13 21 2007 10.1090/S1079-6762-07-00171-0 Sikirić, M.D., Schürmann, A., Vallentin, F.: Classification of eight dimensional perfect forms. Electron. Res. Announc. Amer. Math. Soc 13, 21-32 (2007) 

    상세보기

20. TM Thompson 1983 From Error-Correcting Codes through Sphere Packings to Simple Groups Carus Mathematical Monographs 10.5948/UPO9781614440215 Thompson, T.M.: From Error-Correcting Codes through Sphere Packings to Simple Groups Carus Mathematical Monographs, vol. 21. Mathematical Association of America, Washington (1983) 

    

21. Ann. Math. MS Viazovska 185 3 991 2017 10.4007/annals.2017.185.3.7 Viazovska, M.S.: The sphere packing problem in dimension 8. Ann. Math. 185(3), 991-1015 (2017) 

    상세보기

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