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XVI International Conference Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history dedicated to the 80th anniversary of the birth of Professor Michel Desa
May 14, 2019 09:50–10:35, Tula, TSPU of Leo Tolstoy
 


The Local Theory for Delone and $t$-bonded Sets

Mikhail Bouniaev

University of Texas Rio Grande Valley
Materials:
Adobe PDF 512.0 Kb

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Materials: abstract.pdf (512.0 Kb)

Language: English

References
  1. B.N. Delone, N.P. Dolbilin, M.I. Stogrin, R.V. Galiuilin, “A local criterion for regularity of a system of points”, Soviet Math. Dokl., 17 (1976), 319–322
  2. N.P. Dolbilin, “On Local Properties for Discrete Regular Systems”, Soviet Math. Dokl, 230:3 (1976), 516–519
  3. M. Bouniaev, N. Dolbilin, “Regular and Multi-regular $t$-bonded Systems”, Journal of Information Processing, 21:6 (2017), 735–740, Japan
  4. N. Dolbilin, M. Bouniaev, “Regular $t$-bonded systems in $\mathbb{Z}^3$”, European Journal of Combinatorics, 2018, 1–13
  5. M. Bouniaev, N. Dolbilin, “The local theory for regular systems in the context of $t$-bonded sets”, Symmetry, 10:5 (2018), 159, 1–17, Switzerland
  6. N. Dolbilin, “Identity and Global Symmetry”, Discrete Geometry and Symmetry, Springer Proceedings in Mathematics and Statistics, Springer Int.Pub, 2018
  7. I. Baburin, M. Bouniaev, N. Dolbilin, N. Erochovets, A. Garber, S. Krivovichev, and E. Schulte, “On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets”, Acta Crystallographica, A74 (2018), 616–629
  8. N.P. Dolbilin, A.N. Magazinov, “The Uniqueness Theorem for Locally Antipodal Delone Sets”, Modern Problems of Mathematics, Mechanics and Mathematical Physics, II, Steklov Institute Proc., 294, MAIK, M., 2016, 215–221
  9. L. Danzer, N. Dolbilin, “Delone graphs; some species and local rules”, The mathematics of long-range aperiodic order (Waterloo, ON, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 1997, 85–114
  10. S. Krivovichev, “On the algorithmic complexity of crystals”, Mineralogical Magazine, 78:2 (2014), 415–435
  11. V.Ya Shevchenko, S.V. Krivovichev, and A. Mackay, “Cellular automata and local order in the structural chmistry of the lovozerite group minerals”, Glass Physics and Chemistry, 36 (2010), 1–9


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