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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 13, 2019 10:55–11:40, Tula, TSPU of Leo Tolstoy
 


Convex polytopes, fullerenes and Lobachevsky geometry

V. M. Buchstaberab

a Steklov Mathematical Institute
b Lomonosov Moscow State University
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References
  1. Deza M., Dyutur Sikirich M., Shtogrin M. I., “Fullereny i disk-fullereny”, UMN, 68:4(412) (2013), 69–128
  2. Bukhshtaber V. M., Erokhovets N. Yu., “Konstruktsii semeistv trekhmernykh mnogogrannikov, kharakteristicheskie fragmenty fullerenov i mnogogranniki Pogorelova”, Izv. RAN. Ser. matem, 81:5 (2017), 15–91
  3. Brinkmann G., Goedgebeur J., McKay B. D., “The Generation of Fullerenes”, J. Chem. Inf. Model, 52 (2012), 2910–2918
  4. Buchstaber V. M., Erokhovets N. Yu.,, “Finite sets of operations sufficient to construct any fullerene from $C_{20}$”, Structural Chemistry, 28:1 (2017), 225–234
  5. Pogorelov A. V., “O pravilnom razbienii prostranstva Lobachevskogo”, Matem. zametki., 1:1 (1967), 3–8
  6. Andreev E. M., “O vypuklykh mnogogrannikakh v prostranstvakh Lobachevskogo”, Matem. sb., 81 (123):3 (1970), 445–478
  7. Dǒslić T., “On lower bounds of number of perfect matchings in fullerene graphs”, J. Math. Chem., 24:4 (1998), 359–364
  8. Dǒslić T., “Cyclical edge-connectivity of fullerene graphs and $(k, 6)$-cages”, J. Math. Chem., 33:2 (2003), 103–112
  9. Barnette D., “On generation of planar graphs”, Discrete Mathematics, 7:3-4 (1974), 199–208
  10. Barnette D., “Generating the $c^*$-$5$-connected graphs”, Israel Journal of Mathematics., 28:1-2 (1977), 151–160
  11. Butler, J.W., “A generation procedure for the simple $3$-polytopes with cyclically $5$-connected graphs”, Canad. J. Math., V. XXVI:3 (1974), 686–708
  12. Inoue T., “Organizing volumes of right-angled hyperbolic polyhedra”, Algebr. Geom. Topol, 8:3 (2008), 1523–1565


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