Publications

Research papers

26. A. Glazyrin, R. Karasev, A. Polyanskii, Covering by planks and avoiding zeros of polynomials, to appear in International Mathematics Research Notices.

25. N. Chernega, A. Polyanskii, R. Sadykov, Disjoint edges in geometric graphs, Graphs and Combinatorics, 38, Article number: 162 (2022).

24. O. Pirahmad, A. Polyanskii, A. Vasilevskii, Intersecting diametral balls induced by a geometric graph, to appear in Discrete and Computational Geometry.

23. M. Naszódi, A. Polyanskii, Perron and Frobenius meet Carathéodory, Electronic Journal of Combinatorics, 28(3) (2021), P3.26.

22. A. Kupavskii, A. Polyanskii, I. Tomon, D. Zakharov, The extremal number of surfaces, International Mathematics Research Notices, Volume 2022, Issue 17, 13246-13271.

21. A. Polyanskii, A cap covering theorem, Combinatorica, 41(5) (2021), 695-702.

20. G. Ivanov, M. Naszódi, A. Polyanskii, Approximation of the average of some random matrices , Journal of Functional Analysis 279(7) (2020), 108684.

19. F. Nilov, A. Polyanskii, A Sylvester-Gallai-type Theorem for Abelian Groups, Mathematical Notes, 110 (2021), 110-117.

18. Z. Jiang, A. Polyanskii, Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines, Israel Journal of Mathematics, 236 (2020), 393-421.

17. R. Pinchasi, A. Polyanskii, A one-page solution of a problem of Erdős and Purdy, Discrete and Computational Geometry, 64 (2020), 382–385.

16. A. Polyanskii, On almost-equidistant sets - II, The Electronic Journal of Combinatorics, 26(2) (2019), #P2.14.

15. A.A. Polyanskii, On simultaneous approximations of \ln 3 and \pi/\sqrt{3} by rational numbers, Sbornik:Mathematics, 210(4) (2019), 589-605.

14. A. Polyanskii, On almost-equidistant sets, Linear Algebra and its Applications, 563 (2019), 220-230.

13. A.A. Polyanskii, On the irrationality measures of certain numbers-II, Mathematical Notes, 103(3-4) (2018), 626-634.

12. B.G. Merino, T. Jahn, A. Polyanskii, G. Wachsmuth, Hunting for reduced polytopes, Discrete and Computational Geometry, , 60(3) (2018), 801-808.

11. M. Naszódi, A. Polyanskii, Approximating set multi-covers, European Journal of Combinatorics, 67 (2018), 174-180.

10. A. Kupavskii, A. Polyanskii, Proof of Schur's conjecture in  \mathbb{R}^d, Combinatorica, 37(6) (2017), 1181-1205.

9. A. Polyanskii, Pairwise intersecting homothets of a convex body, Discrete Mathematics, 340(8) (2017), 1950-1956.

8. Z. Jiang,  A. Polyanskii, Proof of László Fejes Tóth's zone conjecture, Geometric and Functional Analysis, 27(6), (2017), 1367–1377.

7. A.B. Kupavskii, A.A. Polyanskii, On simplices in diameter graphs in \mathbb{R}^4, Mathematical Notes, 101(2) (2017), 265-276.

6. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskii, On Schur's conjecture in \mathbb R^4, Mathematical Notes, 97(1) (2015), 21-29.

5. A. Polyanskii, On a question of Makai and Martini on bodies of constant width, Contributions to Algebra and Geometry, 55(2) (2014), 635-636.

4. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskii, Note on Schur's conjecture in \mathbb{R}^4, Doklady Mathematics, 89(1) (2014), 88-91.

3. A.A. Polyanskii, Quadratic irrationality exponents of certain numbers, Moscow University Mathematics Bulletin, 68(5) (2013), 237-240.

2. A.A. Polyanskii, Square exponent of irrationality of \ln 2, Moscow University Mathematics Bulletin, 67(1) (2012), 25-30.

1. A. Polyanskii, On the irrationality measure of certain numbers, Moscow Journal of Combinatorics and Number Theory, 1(4) (2011), 80-90.

Unpublished manuscripts

1. A. Polyanskii, Helly-type theorem for eigenvectors, in preparation.

Expository papers

5. E. Bakaev, G. Chelnokov, A. Polyanskii, Discharging method, Kvant 12 (2019), 31-33 (in Russian).

4. A. Polyanskii, P. Tarasov, Selected examination problems in Discrete Analysis, Matematicheskoe Prosveschenie (2017), 205-209 (in Russian).

3. F. Nilov, A. Polyanskii, N. Polyanskii, The Szemerédi-Trotter theorem, Matematicheskoe Prosveschenie (2017), 186-196 (in Russian).

2. A. Polyanskii, Solving problems without using Pick's formula, Kvant 2 (2013), 40-42 (in Russian).

1. A. Polyanskii, To shoot a cannon with sparrows, Kvant 2 (2012), 49-50, 60-61 (in Russian).

Research projects for Summer Conference of Tournament of Towns

3. E. Bakaev, V. Bulankina, G. Chelnokov, A. Polyanskii, A. Ryabichev, Discharging method, (2019), Aranđelovac, Šumadija District, Serbia (bilingual).

2. F. Nilov, A. Polyanskii, N. Polyanskii, Point-Line Incidences, (2014), Kaliningrad, Russia (bilingual).

1. A. Zaslavskiy, F. Nilov, A. Polyanskii, M. Skopenkov, Webs from lines and circles, (2012), Teberda, Russia (bilingual).

Ph.D. Thesis

1. A.A. Polyanskii, On the irrationality measure of certain numbers (in Russian), Department of Mechanics and Mathematics of Moscow State University, November 2013.