Speciality:
01.01.09 (Discrete mathematics and mathematical cybernetics)
Phone: +7-910-458-88-82
E-mail: Keywords: Polyhedra, the number of topological embeddings 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.
UDC: 519.1, 514 MSC: 05C, 57M, 57N, 51M, 52B, 51F, 20F
Subject:
Combinatorics of tesselations of chessboard with domino tiles: Our recent (2026) algorithm has succeded in calculating the number τ(150 000,8) of domino tilings of the 150 000 x 8 chessboard, and here is the result:
τ(150 000,8) = 13873887020492488...05663089457,
where the whole decimal string has been actually calculated, although only the beginning and end are shown above, with the whole string being of length 143 189.
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.
Main publications:
Magomedov A.M., Lawrence S.A., “An algorithm for counting domino tilings of a rectangular chessboard”, https://doi.org/10.13069/jacodesmath.v13i1.335, Journal of Algebra Combinatorics Discrete Structures and Applications, 13:1 (2026), 15–27.
Lawrence S.A., Magomedov A.M., Chelyapina O.I. and Rudenko V.M., “Combinatorial rigidity and flexibility of simplicial 2-complexes with few vertices”, https://doi.org/10.20429/tag.2025.120102, Theory and Applications of Graphs, 12:1 (2025), Article 2.
Lawrencenko S., Lao A., “Pairs of polyhedra sharing the same 1-skeleton in 3D and 4D spaces, without a single common face”, https://doi.org/10.1080/09720529.2022.2027603, Journal of Discrete Mathematical Sciences and Cryptography, 25:1 (2022), 253–263.
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.
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