lattices and tilings of space,
crystals and quasicrystals,
aperiodic tilings,
polytopes, Rigid and flexible polyhedra,
Ising model,
mathematics education.
Biography
1960–1965 – Department of Mechanics and Mathematics, Moscow State University;
1966– 1969 – graduateship of Steklov Mathematics Institute, Geometry Department;
1969 – present &ndash, leading scientific fellow, Steklov Mathematical Institute of RAS, Department of Geometry and Topology, Laboratory of Popularization and Promotion of Mathematics
Main publications:
A local criterion for regularity of a system of points // Soviet Math. Dokl., 17, 1976, 319–322 (with B. N. Delone, M. I. Stogrin, and R. V. Galiulin).
A local criterion for regularity of a system of points // Soviet Math. Dokl., 17, 1976, 319–322 (with B. N. Delone, M. I. Stogrin, and R. V. Galiulin).
The Countability of a Tiling Family and the Periodicity of Tiling // Discr. and Comput. Geometry, 13, 1995, 405–414.
The Extension Theorem // Discrete Mathematics, 221(1–3), 2000, 43–60.
The two-dimensional Ising model and the Kac–Ward determinant // Izvestiya of Russian Academy of Sciences, Mathematics, 63(4), 1999, 707–727 (jointly with Ju. M. Zinoviev, A. S. Mischenko, M. A. Stanko, and M. I. Stogrin).
Multiregular point systems // Discr. and Comput. Geometry, 20, 1998, 477–498 (jointly with J. C. Lagarias and M. Seneshal).
Nikolay Dolbilin, “Local groups in Delone sets”, Lecture Notes in Computational Sciences and Engineering by Springer International Publishing, vol. 143, https://www.springer.com/book/9783030767976 (2021), 10 pp. (Published online) , arXiv: 2011.00558
2.
Nikolay Dolbilin,, “Foreword to the volume”, Lecture Notes in Computational Sciences and Engineering by Springer International Publishing, 143, https://www.springer.com/book/9783030767976 (2021), 2pp. (Published online)
3.
N. P. Dolbilin, M. I. Shtogrin, “O kristallografichnosti lokalnykh grupp mnozhestva Delone na evklidovoi ploskosti”, Zh. vychisl. matem. i matem. fiz., 2021, 1-12 (to appear)
4.
Nikolay Dolbilin, Alexey Garber, Undine Leopold, Egon Schulte, Marjorie Senechal, “On the regularity radius of Delone sets in $\mathbb R^3$”, Discrete Comput. Geom., 66 (2021), 996–1024 , arXiv: 1909.05805;
2020
5.
Mikhail M. Bouniaev, Nikolay P. Dolbilin, Mikhail I. Shtogrin, “Tilings by hexagonal prisms and embeddings into primitive cubic networks”, Acta Crystallogr. Sect. A, 76:5 (2020), 627–629
2019
6.
N. Dolbilin, M. Bouniaev, “Regular $t$-bonded systems in $R^3$”, European J. Combin., 80 (2019), 89–101 (cited: 1)
7.
N. P. Dolbilin, “Ot lokalnoi identichnosti k globalnomu poryadku”, Diskretnaya matematika i ee prilozheniya, Materialy XIII Mezhdunarodnogo seminara imeni akademika O.B. Lupanova (Moskva, 17-22 iyunya 2019 g.), Izd-vo mekhaniko-matematicheskogo fakulteta MGU, M., 2019 , 10 pp.
8.
N. P. Dolbilin, Kvant, 2019, no. 1, 12–20
9.
V. A. Alexandrov, L. D. Beklemishev, V. M. Buchstaber, A. Yu. Vesnin, A. A. Gaifullin, N. P. Dolbilin, N. Yu. Erokhovets, M. D. Kovalev, V. S. Makarov, S. P. Novikov, D. O. Orlov, A. N. Parshin, I. Kh. Sabitov, D. V. Treschev, O. K. Sheinman, E. V. Shchepin, “Mikhail Ivanovich Shtogrin (on his 80th birthday)”, Russian Math. Surveys, 74:6 (2019), 1159–1162
10.
N. P. Dolbilin, “Geometricheskaya kristallografiya”, Matematicheskaya sostavlyayuschaya, 2-e izd., rassh. i dop., eds. N. N. Andreev, S. P. Konovalov, N. M. Panyunin, Matematicheskie etyudy, M., 2019, 214https://book.etudes.ru/toc/crystallography/
2018
11.
Mikhail Bouniaev, Nikolay Dolbilin, “The local theory for regular systems in the context of $t$-bonded sets”, Symmetry, 10:5 (2018), 159 , 17 pp.
12.
N. P. Dolbilin, “Delone sets in $\mathbb R^3$ with $2R$-regularity conditions”, Proc. Steklov Inst. Math., 302 (2018), 161–185 (cited: 1) (cited: 1)
13.
N. Dolbilin, “Delone Sets: Local Identity and Global Symmetry”, Discrete Geometry and Symmetry, Geometry and Symmetry Conference GSC 2015, Springer Volume dedicated to the 60th anniversary of Professors Karoly Bezdek and Egon Schulte, Springer Proc. Math. Statist., 234, Springer, Cham, 2018, 109–125 (cited: 3) (cited: 4)
14.
I. A. Baburin, M. Bouniaev, N. Dolbilin, N. Yu. Erokhovets, A. Garber, S. V. Krivovichev, E. Schulte, “On the origin of crystallinity: on a lower bound for the regularity radius of Delone sets”, Acta Crystallogr. Sect. A, 74:6 (2018), 616–629 (cited: 8) (cited: 8)
15.
N. P. Dolbilin, Kvant, 2018, no. 12, 2–7
16.
N. P. Dolbilin, “Georgy Feodosevich Voronoy (1868–1908)”, Chebyshevskii Sb., 19:3 (2018), 318–327
2017
17.
Mikhail Bouniaev, Nikolai Dolbilin, “Regular and Multiregular $t$-Systems”, J. Inform. Proc., 25 (2017), 735–740 (cited: 2)
2016
18.
M. M. Bouniaev, N. P. Dolbilin, O. R. Musin, A. S. Tarasov, “Geometrical problems related to crystals, fullerenes, and nanoparticle structure” (Singapore, February 3–4, 2014), Springer Proc. Math. Statist., 124, 2016, 139–151 (cited: 1)
19.
N. P. Dolbilin, A. N. Magazinov, “Uniqueness theorem for locally antipodal Delaunay sets”, Proc. Steklov Inst. Math., 294 (2016), 215–221 (cited: 4) (cited: 5)
20.
Nikolay Dolbilin, “Delone sets with congruent clusters”, Structural Chemistry, 26:6, Dedicated to the 75th anniversary of academician V. Ya. Schevchenko (2016), 1725–1732 (cited: 7) (cited: 10)
21.
Nikolai Dolbilin, Nikolai Andreev, Sergei Konovalov, Nikita Panyunin, “Mathematical Etudes: Evolution from Multimedia to a Book”, Eur. Math. Soc. Newsl., 2016, no. 12, 38–43
22.
N. P. Dolbilin, “Mnozhestva Delone v $\mathbb{R}^3$: uslovie pravilnosti”, Fundament. i prikl. matem., 21:6 (2016), 115–141 (cited: 5) (cited: 5)
2015
23.
N. P. Dolbilin, “Kriterii kristalla i lokalno antipodalnye mnozhestva Delone”, Trudy Mezhdunarodnoi konferentsii “Kvantovaya topologiya”, Vestnik ChelGU, no. 3 (358), 2015, 6–17 (cited: 1) (cited: 2)
24.
N. P. Dolbilin, A. N. Magazinov, “Locally antipodal Delaunay sets”, Russian Math. Surveys, 70:5 (2015), 958–960 (cited: 6) (cited: 7)
25.
N. P. Dolbilin, “The Minkowski Theorem on Parallelohedra and Its Recent Development”, Toric Topology, Number Theory and Applications. Conference Proceedings (Khabarovsk, 6–12 September 2015), Tikhookeanskii gosudarstvennyi universitet, Khabarovsk, 2015, 21–22http://www.iam.khv.ru/ttnt-2015
26.
N. P. Dolbilin, “Geometricheskaya kristallografiya”: N. N. Andreev, S. P. Konovalov, N. M. Panyunin (red.-sost.), v knige “Matematicheskaya sostavlyayuschaya”, Fond “Matematicheskie etyudy”, M., 2015, 110–117
2014
27.
N. P. Dolbilin, H. Edelsbrunner, A. A. Glazyrin, O. R. Musin, “Functionals on Delaunay triangulations”, Mosc. Math. J., 14:3 (2014), 491–504 (cited: 2) (cited: 2) (cited: 1) (cited: 3)
28.
M. Bouniaev, N. Dolbilin, O. Musin, A. Tarasov, “Two groups of geometrical problems related to study of fullerenes & crystals”, Journal of Mathematics, Statistics and Operations Research, 2:2 (2014), 7–22
29.
Gyunter M. Tsigler, Teoriya mnogogrannikov, perevod s angliiskogo pod redaktsiei N. P. Dolbilina, MTsNMO, M., 2014 , 565 pp., Predislovie redaktora perevoda
30.
N. N. Andreev, N. P. Dolbilin, S. P. Konovalov, N. M. Panyunin, “Mathematical Etudes: A Russian Tradition in New Form”, Math. Intell., 36:3 (2014), 47–52
2013
31.
N. Dolbilin, Jin-ichi Itoh, Chie Nara, “Affine classes of 3-dimensional parallelohedra - Their parametrization”, Computational geometry and graphs, Lecture Notes in Computer Science, 8296, eds. J. Akiyama, M. Kano, T. Sakai, Springer-Verlag, Berlin–Heidelberg, 2013, 64–72
32.
N. P. Dolbilin, “Delone Sets and Polyhedral Tilings: Local Rules and Global Order”, 10 International Symposium on Voronoi Diagrams in Science (ISVD 2013), Program and Abstracts (Saint Petersburg, July 8–10, 2013), St. Petersburg Academic University, 2013, 3
33.
N. Dolbilin, “Parallelohedra: from Minkowski and Voronoi to the present day”, The 2nd Pasific Rim Mathematical Association Congress, Program and Abstracts (June 24–28, 2013, Shanghai, China), Shanghai Jiao Tong University, Shanghai, 2013, 9–10
34.
M. Bouniaev, N. Dolbilin, “Local rules and global order in crystals”, XII International Symposium on Self-propagating High-Temperature Synthesis, Book of Abstracts (21–24 October, 2013, South Padre Island, Texas, USA), University of Texas at Brownsvill, 2013, 306–307
35.
M. Bouniaev, N. Dolbilin, “Local Rules as the Mechanism of Global Order Formation in Crystals”, Fifth International Conference on Analytic Number Theory and Spatial Tessellations, devoted to the development of a scientic heritage of G. Voronoi (1868–1908) (Kyiv, National Pedagogical Dragomanov University, 16–20 September, 2013), Institute of Mathematics, NAS of Ukraine, Kyiv, 2013, 60–61http://www.mathematik.uni-wuerzburg.de/~oswald/voronoiconf.pdf
36.
N. P. Dolbilin, “Parallelohedra and the Voronoi Conjecture”, Algebraic Topology and Abelian Functions. Abstracts, Conference in honour of Victor Buchstaber on the occasion of his 70th birthday (Moscow, Steklov Mathematical Institute of RAS, 18–22 June 2013), Steklov Mathematical Institute, 2013, 37–38http://vmb70.mi.ras.ru/abstracts.pdf
2012
37.
N. P. Dolbilin, O. R. Musin, H. Edelsbrunner, “On the optimality of functionals over triangulations of Delaunay sets”, Russian Math. Surveys, 67:4 (2012), 781–783 (cited: 2) (cited: 2) (cited: 2) (cited: 3)
38.
N. P. Dolbilin, Trans. Moscow Math. Soc., 2012, 207–220 (cited: 3)
39.
N. Dolbilin, H. Edelsbrunner, A. Ivanov, O. Musin, “The First Yaroslavl Summer School on Discrete and Computational Geometry”, Model. Anal. Inform. Sist., 19:4 (2012), 168–173
40.
N. Dolbilin, H. Edelsbrunner, A. Ivanov, O. Musin, M. Nevskii, “Yaroslavl International Conference on Discrete Geometry (dedicated to the centenary of A. D. Alexandrov)”, Model. i analiz inform. sistem., 19:6 (2012), 92–100
2011
41.
N. Dolbilin, Jin-ichi Itoh, Chie Nara, “Affine equivalent classes of parallelohedra”, Computational geometry, graphs and applications, 9th International conference, CGGA 2010 (Dalian, China, November 3–6, 2010), Revised selected papers, Lecture Notes in Comput. Sci., 7053, eds. Jin Akiyama, et al., Springer, Heidelberg, 2011, 55–60 (cited: 3) (cited: 2) (cited: 5)
42.
N. Dolbilin, “Local rules and global order”, Foundations in crystallography, Abstracts of the XXII International Union of Crystallography (Madrid, Spain, 22–30 August 2011), Acta Crystallographica, A67, Wiley, New York, 2011, 184–185
43.
N. P. Dolbilin, “Boris Nikolaevich Delone (Delaunay): life and work”, Proc. Steklov Inst. Math., 275 (2011), 1–14 (cited: 2) (cited: 2) (cited: 2) (cited: 1)
2010
44.
N. Dolbilin, D. Frettlöh, “Properties of Böröczky tilings in high-dimensional hyperbolic spaces”, European J. Combin., 31:4 (2010), 1181–1195 , arXiv: 0705.0291 (cited: 3) (cited: 2) (cited: 3)
45.
N. P. Dolbilin, M. A. Kozachok, “Polytopes with centrally symmetric faces”, Chebyshev Sb., XI:1(33) (2010), 109–115
N. P. Dolbilin, “Properties of Faces of Parallelohedra”, Proc. Steklov Inst. Math., 266 (2009), 105–119 (cited: 9) (cited: 5) (cited: 5) (cited: 6)
49.
N. Dolbilin, E. Schulte, “A local characterization of combinatorial multihedrality in tilings”, Contrib. Discrete Math., 4:1 (2009), 1–11 , arXiv: 0809.2291
2008
50.
N. P. Dolbilin, “The Voronoi problem and the Minkowski theorems on parallelohedra”, Numerical geometry, grid generation and high performance computing, Russ. Acad. Sci., Dorodnicyn Comput. Cent., Moscow, 2008, 190–195
51.
N. Dolbilin, M. Tanemura, “Voronoi tilings on the Clifford torus in a 3-sphere”, Voronoi's impact on the modern science 4, v. 1, NAN of Ukraine, Kyiv, 2008, 210–219
52.
N. Dolbilin, E. Schulte, “Special issue in honor of Ludwig Danzer's 80th birthday (Foreword)”, European J. Combin., 29:8 (2008), 1801–1802
53.
V. A. Aleksandrov, Yu. A. Aminov, V. M. Buchstaber, V. A. Vassiliev, N. P. Dolbilin, S. P. Novikov, Yu. G. Reshetnyak, V. A. Sadovnichii, V. T. Fomenko, “Idzhad Khakovich Sabitov (on his 70th birthday)”, Russian Math. Surveys, 63:6 (2008), 1173–1177
54.
N. Dolbilin, Kvant, 2008, no. 1, 9–14
2007
55.
N. P. Dolbilin, “Minkowski's theorems on parallelohedra and their generalisations”, Russian Math. Surveys, 62:4 (2007), 793–795 (cited: 4) (cited: 2) (cited: 2) (cited: 3)
2006
56.
N. Dolbilin, M. Tanemura, “How many facets on average can a tile have in a tiling?”, Forma, 21:3 (2006), 177–196
57.
N. P. Dolbilin, A. A. Maltsev, “Sergei Sergeevich Ryshkov”, Chebyshevskii sb., 7:2(18) (2006), 4–12
58.
N. Dolbilin, Kvant, 2006, no. 4, 2–8
2005
59.
N. Dolbilin, M. Tanemura, “On tilings whose tiles have many facets”, Rev. Roumaine Math. Pures Appl., 50:5-6 (2005), 595–611
2004
60.
N. Dolbilin, E. Schulte, “The local theorem for monotypic tilings”, Electron. J. Combin., 11:2 (2004), Research Paper 7 , 19 pp. (cited: 4)
2002
61.
N. P. Dolbilin, V. S. Makarov, “Extension Theorem in the Theory of Isohedral Tilings and Its Applications”, Proc. Steklov Inst. Math., 239 (2002), 136–158
62.
E. P. Baranovskii, N. P. Dolbilin, A. A. Mal'tsev, “Sergei Sergeevich Ryshkov (On his 70th Birthday)”, Proc. Steklov Inst. Math., 239 (2002), 1–12
2001
63.
N. Dolbilin, “Tri teoremy o vypuklykh mnogogrannikakh”, Kvant, 5,6 (2001), 7–12, 3–10
2000
64.
N. P. Dolbilin, “The extension theorem”, Discrete Math., 221:1-3, Selected papers in honor of Ludwig Danzer (2000), 43–59 (cited: 6) (cited: 9) (cited: 7)
65.
N. Dolbilin, “Self-similar mosaics”, Quantum, 10:6 (2000), 4–9
66.
N. P. Dolbilin, Pearls of the theory of polyhedra, Mathematical Enlighting Library, 5, Moscow Center of Continuous Education Center Publishing House, Moscow, 2000 , 40 pp.
1999
67.
N. P. Dolbilin, Yu. M. Zinoviev, A. S. Mishchenko, M. A. Shtan'ko, M. I. Shtogrin, “The two-dimensional Ising model and the Kac–Ward determinant”, Izv. Math., 63:4 (1999), 707–727 (cited: 4) (cited: 2)
68.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Rigidity of a quadrillage of the torus”, Russian Math. Surveys, 54:4 (1999), 839–840 (cited: 4) (cited: 1) (cited: 2)
69.
N. P. Dolbilin, Yu. M. Zinoviev, A. S. Mishchenko, M. A. Shtan'ko, M. I. Shtogrin, “The Kac–Ward Determinant”, Proc. Steklov Inst. Math., 225 (1999), 165–182
1998
70.
N. P. Dolbilin, J. C. Lagarias, M. Senechal, “Multiregular point systems”, Discrete Comput. Geom., 20:4 (1998), 477–498 (cited: 29) (cited: 23) (cited: 35)
71.
N. P. Dolbilin, “Rigidity of convex polyhedrons”, Quantum, 9:1 (1998), 8–13
72.
D. Schattschneider, N. Dolbilin, “One corona is enough for the Euclidean plane”, Quasicrystals and discrete geometry (Toronto, ON, 1995), Fields Inst. Monogr., 10, Amer. Math. Soc., Providence, RI, 1998, 207–246
73.
N. Dolbilin, D. Schattschneider, “The local theorem for tilings”, Quasicrystals and discrete geometry (Toronto, ON, 1995), Fields Inst. Monogr., 10, Amer. Math. Soc., Providence, RI, 1998, 193–199
74.
N. P. Dolbilin, A. W. M. Dress, D. H. Huson, “Two finiteness theorems for periodic tilings of $d$-dimensional Euclidean space”, Discrete Comput. Geom., 20:2 (1998), 143–153 (cited: 2) (cited: 1) (cited: 2)
75.
N. P. Dolbilin, Yu. M. Zinoviev, M. A. Shtan'ko, M. I. Shtogrin, “The Kac–Ward combinatorial method”, Russian Math. Surveys, 53:6 (1998), 1346–1347 (cited: 3) (cited: 3)
76.
N. P. Dolbilin, “Which clusters can form a crystal?”, Voronoi's impact on modern science, Book 2, eds. P. Engel (Switzerland), H. Syta (Ukraine), Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, 1998, 96–104
1997
77.
N. P. Dolbilin, D. H. Huson, “Periodic Delone tilings”, 3rd Geometry Festival: an International Conference on Packings, Coverings and Tilings (Budapest, 1996), Period. Math. Hungar., 34, no. 1-2, 1997, 57–64 (cited: 2) (cited: 13)
78.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Nonbendability of a division of a sphere into squares”, Dokl. Math., 55:3 (1997), 385–387 (cited: 2)
79.
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., 489, Kluwer Acad. Publ., Dordrecht, 1997, 85–114 (cited: 3)
80.
N.P. Dolbilin, “Igra “Khaos” i fraktaly”, Kvant, 4 (1997), 2–9
1996
81.
N. P. Dolbilin, Yu. M. Zinoviev, A. S. Mishchenko, M. A. Shtan'ko, M. I. Shtogrin, “Homological Properties of Dimer Configurations for Lattices on Surfaces”, Funct. Anal. Appl., 30:3 (1996), 163–173 (cited: 13) (cited: 10) (cited: 14)
82.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “On rigidity of polyhedral spheres with even-angle faces”, Russian Math. Surveys, 51:3 (1996), 543–544 (cited: 2) (cited: 1)
83.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Rigidity of zonohedra”, Russian Math. Surveys, 51:2 (1996), 326–328 (cited: 2) (cited: 1)
1995
84.
N. Dolbilin, “The countability of a tiling family and the periodicity of a tiling”, Discrete Comput. Geom., 13:3-4 (1995), 405–414 (cited: 5) (cited: 3) (cited: 6)
85.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Cubic manifolds in lattices”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 301–313 (cited: 13) (cited: 9)
1993
86.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Quadrillages and parametrizations of lattice cycles”, Proc. Steklov Inst. Math., 193 (1993), 117–123
1992
87.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Quadrillages and parametrizations of lattice cycles”, Proc. Steklov Inst. Math., 196 (1992), 73–93
88.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “Combinatorial questions of the two-dimensional Ising model”, Proc. Steklov Inst. Math., 196 (1992), 57–72
1991
89.
E. P. Baranovskii, N. P. Dolbilin, V. S. Makarov, A. A. Mal'tsev, S. P. Novikov, M. I. Shtogrin, “Sergei Sergeevich Ryshkov (on his sixtieth birthday)”, Russian Math. Surveys, 46:3 (1991), 263–266
1992
90.
D. K. Faddeev, N. P. Dolbilin, S. S. Ryshkov, M. I. Shtogrin, “Boris Nikolaevich Delone. On his life and creative work”, Proc. Steklov Inst. Math., 196 (1992), 1–9
1990
91.
N. P. Dolbilin, “Boris Nikolaevich Delone (on the centennial of his birth)”, Matematika v shkole, 1990, no. 1, i, 68–70
1988
92.
I. Bárány, N. P. Dolbilin, “A stability property of the densest circle packing”, Monatsh. Math., 106:2 (1988), 107–114 (cited: 5) (cited: 5)
1989
93.
N. P. Dolbilin, M. A. Shtan'ko, M. I. Shtogrin, “The problem of parametrization of cycles modulo 2 in a three-dimensional cubic lattice”, Math. USSR-Izv., 32:2 (1989), 359–383
1988
94.
N. P. Dolbilin, M. I. Shtogrin, “Lokalnyi kriterii dlya kristallicheskikh struktur”, Tezisy IX Vsesoeznoi Geometricheskoi konferentsii (Kishinev, 1988), Institut matematiki AN MSSR, 1988, s. 99
95.
N. P. Dolbilin, “Zhestkost vypuklykh mnogogrannikov”, Kvant, 5 (1988), 6–14 http://kvant.mccme.ru/au/dolbilin_n.htm
1987
96.
N. P. Dolbilin, “A characteristic of lattices and the inhomogeneous Minkowski problem”, Studia Sci. Math. Hungar., 22:1-4 (1987), 107–113
1988
97.
N. P. Dolbilin, A. G. Sedrakyan, M. A. Shtan'ko, M. I. Shtogrin, “A topology for the family of parametrizations of two-dimensional cycles arising in the three-dimensional Ising model”, Soviet Math. Dokl., 36:1 (1988), 11–15 (cited: 6)
1986
98.
N. P. Dolbilin, M. A. Shtanko, M. I. Shtogrin, “Kubicheskie podkompleksy v pravilnykh reshetkakh”, Dokl. AN SSSR, 291:2 (1986), 277–279 (cited: 7) (cited: 5)
99.
N. P. Dolbilin, “Pik Delone”, Kvant, 3 (1986), 10–16 http://kvant.mccme.ru/1986/03/pik_delone.htm
1980
100.
B. N. Delone, N. P. Dolbilin, M. I. Shtogrin, “Combinatorial and metric theory of planigons”, Proc. Steklov Inst. Math., 148 (1980), 111–141
1978
101.
N. P. Dolbilin, Symmetry, News in Science, Znanie [Knowledge] Publishing House, Moscow, 1978 , 65 pp.
1976
102.
N. P. Dolbilin, “O lokalnykh svoistvakh diskretnykh pravilnykh sistem”, Dokl. AN SSSR, 230:3 (1976), 516–519 (cited: 4) (cited: 5)
103.
B. N. Delone, N. P. Dolbilin, M. I. Shtogrin, R. V. Galiulin, “Lokalnyi kriterii pravilnosti sistemy tochek”, Dokl. AN SSSR, 227:1 (1976), 19–21 (cited: 12) (cited: 35)
1974
104.
N. P. Dolbilin, “The covering radius of hyperbolically equivalent $n$-dimensional lattices, and the boundedness of the index of a divided parallelepiped”, Dokl. AN SSSR, 214 (1974), 1002–1004
1973
105.
B. N. Delone, R. V. Galiulin, N. P. Dolbilin, V. A. Zalgaller, M. I. Štogrin, “Three successive minima of a three-dimensional lattice”, Dokl. AN SSSR, 209 (1973), 25–28
1971
106.
N. P. Dolbilin, “On 3- and 4-dimensional simple forms”, Problems of Crystallology, Collected papers dedicated to 80-anniversary of academician N. V. Belov, MSU Publishing House, Moscow, 1971, 315–323
1970
107.
B. N. Delone, N. P. Dolbilin, S. S. Ryshkov, M. I. Shtogrin, “A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres”, Math. USSR-Izv., 4:2 (1970), 293–302 (cited: 2)
Presentations in Math-Net.Ru
1.
On Crystallinity of $2R$-isometric Delone Sets: New Results and Open Problems Nikolay Dolbilin 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 09:00
Delone sets and the regularity radius N. P. Dolbilin XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 09:50
4.
Locally Isometric Delone Sets Nikolay P. Dolbilin International conference "Algebraic Topology, Combinatorics, and Mathematical Physics" on occasion of Victor Buchstaber's 75th birthday May 29, 2018 10:00
On the regular systems N. P. Dolbilin А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications May 26, 2017 13:20
9.
Locally Antipodal Delone Sets N. P. Dolbilin Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications January 28, 2016 15:00
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Круглый стол «Геометрия в школе» N. P. Dolbilin, V. M. Tikhomirov Conference "Moscow Mathematical Society and Lomonosov Moscow State University" dedicated to the 150th anniversary of Moscow Mathematical Society December 25, 2014 11:30
Parallelohedra and the Voronoi Conjecture Nikolay Dolbilin International conference "Algebraic Topology and Abelian Functions" in honour of Victor Buchstaber on occasion of his 70th birthday June 18, 2013 15:50
2021
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