Publications

In preparation

26. A. Polyanskii, R. Sadykov, New generalizations of the Alon-Boppana Theorem.

25. N. Chernega, A. Polyanskii, R. Sadykov, Non-crossings in geometric graphs.

Research papers

24. M. Naszódi, A. Polyanskii, Perron and Frobenius meet Carathéodory, submited.

24. A. Kupavskii, A. Polyanskii, I. Tomon, D. Zakharov, The extremal number of surfaces, submited.

23. A. Polyanskii, A cap covering theorem, Combinatorica, accepted.

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

21. F. Nilov, A. Polyanskii, A Sylvester-Gallai-type theorem in abelian groups, submitted.

19. 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.

18. R. Pinchasi, A. Polyanskii, A one-page solution of a problem of Erdős and Purdy, Discrete and Computational Geometry, (2019).

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

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

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 widthContributions 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 numbersMoscow Journal of Combinatorics and Number Theory, 1(4) (2011), 80-90.

Expository papers

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, 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

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

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