Polyhedra, the number of topological embedding of a graph in a surface and the number of geometric polyhedra with a given 1-skeleton. The 4-genus of the complete graph. Even Map Color Theorem. Irreducible triangulations of surfaces.
Polyhedra: Geometric realizations of abstract complexes, symmetries, discrete isoperimetric constants, volume equations for polyhedra. Mathematical modeling, flexibility of embeddings and polyhedra, triangulations of 2-, 3-, and 4-manifolds, irreducible triangulations,
coloring of graphs,
reliable networks,
spinal quadrangulations,
homology of polyhedra,
algorithms and optimization. The 4-genus of the complete graph, Even Map Color Theorem.
Biography
I am a member of the American Mathematical Society, the author of a pair of toroidal polyhedra (each without self-intersections) in 3-space, with the same geometric skeleton but without a single face in common.
I am the author of more than a hundred research papers on discrete mathematics, discrete geometry, and service, of which 60 are peer-reviewed articles in 32 scientific journals of the world. In particular, I am the author of the irreducible triangulations of the torus and the Klein bottle (in coauthorship with Seiya Negami); the author of the 4-genus of the complete graph and the Even Map Color Theorem (with coauthors).
I hold the Ph.D. in mathematics from Moscow State University, 1990, in the former Soviet Union. I am an author and lecturer. I have published a good number of research papers on discrete mathematics, computer science, geometry and topology.
I have delivered invited lectures at conferences and universities in 3 continents, in 10 countries to date, including lectures in four federal districts of Russia, three provinces of China as well as Hong Kong, Beijing, and Shanghai, and four states of the USA as well as Washington DC.
Main publications:
Lawrencenko S., “Polyhedral suspensions of arbitrary genus”, https://doi.org/10.1007/s00373-010-0938-5, Graphs and Combinatorics, 26:4 (2010), 537–548.
Harianto B.B., Al-Awsi G.R.L., Sivaraman R., Anarboev M., Ponkratov V.V., Lawrencenko S., Aravindhan S., Bloshenko T.A., Muda I., “Development of a hybrid system model for enhanced lifespan, energy efficiency, and power quality in fuel cells”, https://doi.org/10.18280/mmep.100318, Mathematical Modelling of Engineering Problems, 10:3 (2023), 879–885.
Lawrencenko S., Magomedov A.M., “Generating the triangulations of the torus with the vertex-labeled complete 4-partite graph K_{2,2,2,2}”, https://doi.org/10.3390/sym13081418, Symmetry, 13:8 (2021), Paper No. 1418.
Liu W., Lawrencenko S., Chen B., Ellingham M.N., Hartsfield N., Yang H., Ye D., Zha X., “Quadrangular embeddings of complete graphs and the Even Map Color Theorem”, https://doi.org/10.1016/j.jctb.2019.02.006, Journal of Combinatorial Theory, Series B, 139 (2019), 1–26.
S. Lawrence, A. S. Lao, M. E. Lao, O. I. Chelyapina, “Pairs of mutually complementary $2$-dimensional simplicial polyhedra: Interesting examples”, Chebyshevskii Sb., 24:3 (2023), 42–55
2021
2.
A. M. Magomedov, S. Lawrencenko, “Computational algorithm for enumerating graphs of a given order”, Daghestan Electronic Mathematical Reports, 2021, no. 16, 1–15
2020
3.
A. M. Magomedov, S. Lawrencenko, “Computational aspects of the partition enumeration problem”, Daghestan Electronic Mathematical Reports, 2020, no. 14, 1–21
4.
A. M. Magomedov, S. Lawrencenko, “Solving puzzles by O. Ore's method”, Daghestan Electronic Mathematical Reports, 2020, no. 13, 22–30
2019
5.
A. M. Magomedov, S. Lawrencenko, “Some aspects of familiarization with binomial coefficients”, Daghestan Electronic Mathematical Reports, 2019, no. 11, 49–53
6.
A. M. Magomedov, T. A. Magomedov, S. A. Lawrencenko, “Mutually-recursive formulas for enumerating partitions of the rectangle”, Prikl. Diskr. Mat., 2019, no. 46, 108–121
A. M. Magomedov, S. Lawrencenko, “Automation of the creation of test units by programming language”, Daghestan Electronic Mathematical Reports, 2018, no. 9, 76–80
8.
S. Lawrencenko, T. Sulanke, M. T. Villar, L. V. Zgonnik, M. J. Chávez, J. R. Portillo, “Irreducible triangulations of the once-punctured torus”, Sib. Èlektron. Mat. Izv., 15 (2018), 277–304
S. Lawrencenko, A. Yu. Shchikanov, “Euclidean realization of the product of cycles without hidden symmetries”, Sib. Èlektron. Mat. Izv., 12 (2015), 777–783
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