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Dolbilin Nikolai Petrovich
(recent publications)

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2022
1.	N. P. Dolbilin, M. I. Shtogrin, “Mnozhestva i razbieniya Delone: lokalnyi podkhod”, Toricheskaya topologiya, deistviya grupp, geometriya i kombinatorika. Chast 2, Sbornik statei, Trudy MIAN, 318, MIAN, M., 2022, 73–98
2.	N. P. Dolbilin, M. I. Shtogrin, “Crystallographic properties of local groups of a Delone set in a Euclidean plane”, Comput. Math. Math. Phys., 62:8 (2022), 1265–1274
3.	N. P. Dolbilin, M. I. Shtogrin, “Local groups in Delone sets in the Euclidean space”, Acta Crystallogr. Sect. A, 78 (2022), 452–478

2021
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 (cited: 3) (cited: 2);
5.	Nikolay Dolbilin, “Local groups in Delone sets”, Numerical Geometry, Grid Generation and Scientific Computing, Lect. Notes Comput. Sci. Eng., 143, Springer, Cham, 2021, 3–11 , arXiv: 2011.00558 (cited: 1);
6.	N. P. Dolbilin, M. I. Shtogrin, “Local groups in Delone sets: a conjecture and results”, Russian Math. Surveys, 76:6 (2021), 1137–1139 (cited: 1)

2020
7.	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
8.	N. Dolbilin, M. Bouniaev, “Regular $t$-bonded systems in $R^3$”, European J. Combin., 80 (2019), 89–101 (cited: 1) (cited: 2)
9.	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.

2018
10.	Mikhail Bouniaev, Nikolay Dolbilin, “The local theory for regular systems in the context of $t$-bonded sets”, Symmetry, 10:5 (2018), 159 , 17 pp.
11.	N. P. Dolbilin, “Delone sets in $\mathbb R^3$ with $2R$-regularity conditions”, Proc. Steklov Inst. Math., 302 (2018), 161–185 (cited: 4) (cited: 4)
12.	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: 5)
13.	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: 12) (cited: 12)

2017
14.	Mikhail Bouniaev, Nikolai Dolbilin, “Regular and Multiregular $t$-Systems”, J. Inform. Proc., 25 (2017), 735–740 (cited: 4)

2016
15.	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)
16.	N. P. Dolbilin, A. N. Magazinov, “Uniqueness theorem for locally antipodal Delaunay sets”, Proc. Steklov Inst. Math., 294 (2016), 215–221 (cited: 4) (cited: 6)
17.	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: 9) (cited: 13)
18.	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
19.	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
20.	N. P. Dolbilin, “Kriterii kristalla i lokalno antipodalnye mnozhestva Delone”, Trudy Mezhdunarodnoi konferentsii “Kvantovaya topologiya”, Vestnik ChelGU, no. 3 (358), 2015, 6–17 (cited: 3) (cited: 2)
21.	N. P. Dolbilin, A. N. Magazinov, “Locally antipodal Delaunay sets”, Russian Math. Surveys, 70:5 (2015), 958–960 (cited: 6) (cited: 7)
22.	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, 21–22 http://www.iam.khv.ru/ttnt-2015

2014
23.	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)
24.	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

2013
25.	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
26.	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
27.	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
28.	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
29.	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, 60–61 http://www.mathematik.uni-wuerzburg.de/~oswald/voronoiconf.pdf
30.	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, 37–38 http://vmb70.mi.ras.ru/abstracts.pdf

2012
31.	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)
32.	N. P. Dolbilin, Trans. Moscow Math. Soc., 2012, 207–220 (cited: 5)
33.	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
34.	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
35.	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)
36.	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

2010
37.	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)
38.	N. P. Dolbilin, M. A. Kozachok, “Polytopes with centrally symmetric faces”, Chebyshev Sb., XI:1(33) (2010), 109–115

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