Vsevolod F. Lev

Publications List


A. Papers in the Theory of Uniform Distribution
B. Papers in Combinatorial Number Theory and Group Theory
C. Popular Papers and Problems
D. Other Papers

    A. Papers in the Theory of Uniform Distribution

  1. Hyperbolic zeta-function of general form, Mat. Zametki 48 (5) (1990), 148–150 [Russian].

  2. Diaphony and quadratic discrepancies of multidimensional nets, Mat. Zametki 47 (6) (1990), 45–54 [Russian]. English translation in: Math. Notes 47 (5–6) (1990), 556–564.

  3. Quadrature formulas for classes with restrictions on Fourier coefficients, Mat. Zametki 49 (2) (1991), 144–147 [Russian]. English translation in: Math. Notes 49 (1–2) (1991), 219–221.

  4. On two versions of L2-discrepancy and geometrical interpretation of diaphony, Acta Mathematica Hungarica 69 (4) (1995), 235–254.

  5. Translations of nets and relationship between Supreme and Lp-discrepancies, Acta Mathematica Hungarica 70 (1–2) (1996), 1–12.

  6. Discrepancy of weighted matrix nets (with William Chen), Acta Arithmetica 85 (2) (1998), 141–156.

  7. The exact order of generalized diaphony and multidimensional numerical integration, Journal of the Australian Mathematical Society, Series A 66 (1999), 1–17.

    B. Papers in Combinatorial Number Theory and Group Theory

  8. On addition of two distinct sets of integers, (with Pavel Smeliansky), Acta Arithmetica 70 (1) (1995), 85–91.

  9. Representing powers of 2 by a sum of four integers, Combinatorica 16 (3) (1996), 413–416.

  10. Representation of elements of a sequence by sumsets, Combinatorica 16 (4) (1996), 587–590.

  11. On the extremal aspect of Frobenius problem, Journal of Combinatorial Theory, Series A 73 (1) (1996), 111–119.

  12. Structure theorem for multiple addition and the Frobenius problem, Journal of Number Theory 58 (1) (1996), 79–88.

  13. Addendum to "Structure theorem for multiple addition", Journal of Number Theory 65 (1) (1997), 96–100.

  14. Optimal representations by sumsets and subset sums, Journal of Number Theory 62 (1) (1997), 127–143.

  15. On consecutive subset sums, Discrete Mathematics 187 (1–3) (1998), 151–160.

  16. Rectification principles in additive number theory (with Yuri Bilu and Imre Ruzsa), Discrete Computational Geometry 19 (3) (1998), 343–353.

  17. On the number of solutions of a linear equation over finite sets of integers, Journal of Combinatorial Theory, Series A 83 (2) (1998), 251–267.

  18. The structure of multisets with a small number of subset sums, Astèrisque 258 (1999), 179–186.

  19. On small sumsets in abelian groups, Astèrisque 258 (1999), 317–321.

  20. Greedy algorithm, arithmetic progressions, subset sums and divisibility (with P. Erdős, G. Rauzy, C. Sándor and A. Sárközy), Discrete Mathematics 200 (1999), 119–135.

  21. Simultaneous approximations and covering by arithmetic progressions in Fp, Journal of Combinatorial Theory, Series A 92 (2) (2000), 103–118.

  22. Combinatorics and linear algebra of Freiman's isomorphism (with Sergei Konyagin), Mathematika 47 (2000), 39–51.

  23. Restricted set addition in groups, I. The classical setting, Journal of the London Mathematical Society 62 (1) (2000), 27–40.

  24. Restricted set addition in groups, II. A generalization of Erdős-Heilbronn conjecture, The Electronic Journal of Combinatorics 7 (2000), #R4.

  25. Restricted set addition in groups, III. Integer sumsets with generic restrictions, Periodica Math. Hungarica 42 (1–2) (2001), 89–98.

  26. Sum-free sets in abelian groups (with Tomasz Łuczak and Tomasz Schoen), Israel Journal of Mathematics 125 (2001), 347–367.

  27. Cameron-Erdős modulo a prime (with Tomasz Schoen), Finite Fields and their Applications, 8 (1) (2002), 108–119.

  28. Three-fold restricted set addition in groups, European Journal of Combinatorics 23 (5) (2002), 613–617.

  29. Sharp estimates for the number of sum-free sets, Journal für die reine und angewandte Mathematik (Crelle's Journal) 555 (2003), 1–25.

  30. Blocks and progressions in subset sum sets, Acta Arithmetica 106 (2) (2003), 123–142.

  31. How long does it take to generate a group? (with Benjamin Klopsch), Journal of Algebra 261 (2003), 145–171.

  32. Generating binary spaces, Journal of Combinatorial Theory, Series A 102 (1) (2003), 94–109.

  33. Progression-free sets in finite abelian groups, Journal of Number Theory 104 (1) (2004), 162–169.

  34. Reconstructing integer sets from their representation functions, The Electronic Journal of Combinatorics 11 (1) (2004), #R78.

  35. Restricted set addition in abelian groups: results and conjectures, Journal de Théorie des Nombres de Bordeaux (Journées Arithmétiques 2003 special issue) 17 (1) (2005), 181–193.

  36. Large sum-free sets in ternary spaces, Journal of Combinatorial Theory, Series A 111 (2) (2005), 337–346.

  37. The continuous postage stamp problem, Journal of the London Mathematical Society 73 (3) (2006), 625–638.

  38. Permutations in abelian groups and the sequence n!(mod p), European Journal of Combinatorics 27 (5) (2006), 635–643.

  39. Large sum-free sets in Z/pZ, Israel Journal of Mathematics 154 (2006), 221–234.

  40. Critical pairs in abelian groups and Kemperman's theorem, International Journal of Number Theory 2 (3) (2006), 379–396.

  41. On sum-free subsets of the torus group, Functiones et Approximatio XXXVII (2) (2007), 277–283.

  42. Open problems in additive combinatorics (with Ernie Croot), in: CRM Proc. Lecture Notes 43, Amer. Math. Soc., Providence, RI (2007), 207–233.

  43. The connectivity of addition Cayley graphs [extended abstract of the talk at the European Conference on Combinatorics, Graph Theory and Applications] (with David Grynkiewicz and Oriol Serra), Electronic Notes in Discrete Mathematics 29 (2007), 135–139.

  44. Sums and differences along hamiltonian cycles [extended abstract of the talk at the Sixth Czech-Slovak International Symposium on Combinatorics], Electronic Notes in Discrete Mathematics 28 (2007), 25–31.

  45. Sums and differences along hamiltonian cycles, Discrete Mathematics 310 (3) (2010) (Sixth Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications special volume), 575–584.

  46. Powers of 2 with five distinct summands, Acta Arithmetica 132 (3) (2008), 197–204.

  47. The rectifiability threshold in abelian groups, Combinatorica 28 (4) (2008), 491–497.

  48. Generating abelian groups by addition only (with Benjamin Klopsch), Forum Mathematicum 21 (1) (2009), 23–41.

  49. A refined bound for sum-free sets in groups of prime order (with Jean-Marc Deshouillers), Bulletin of the London Mathematical Society 40 (5) (2008), 863–875.

  50. Connectivity of addition Cayley graphs (with David Grynkiewicz and Oriol Serra), Journal of Combinatorial Theory, Series B 99 (2009), 202–217.

  51. On the number of popular differences (with Sergei Konyagin), Israel Journal of Mathematics 176 (2010), 269–283.

  52. Consecutive integers in high-multiplicity sumsets, Acta Mathematica Hungarica 129 (3) (2010), 245–253.

  53. Additive bases in abelian groups (with Mikhail E. Muzychuk and Rom Pinchasi), International Journal of Number Theory 6 (4) (2010), 799–809.

  54. The Erdős-Turán problem in infinite groups (with Sergei Konyagin), in: D. Chudnovsky and G. Chudnovsky (Editors), "Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson", Springer (2010).

  55. 1-saturating sets, caps, and doubling-critical sets in binary spaces (with David Grynkiewicz), SIAM Journal on Discrete Mathematics 24 (1) (2010), 169–190.

  56. Translation invariance in groups of prime order, Journal of Number Theory 131 (2011), 1827–1832.

  57. An Erdős-Fuchs type theorem for finite groups (with András Sárközy), INTEGERS: The Electronic Journal of Combinatorial Number Theory 11 (4) (2011), 487–494.

  58. Character-free approach to progression-free sets, Finite Fields and their Applications 18 (2) (2012), 378–383.

  59. Kakeya-type sets in finite vector spaces (with Swastik Kopparty, Shubhangi Saraf, and Madhu Sudan), Journal of Algebraic Combinatorics 34 (3) (2011), 337–355.

  60. On the size of dissociated bases (with Raphael Yuster), The Electronic Journal of Combinatorics 18 (1) (2011), #P117.

  61. Small asymmetric sumsets in elementary abelian 2-groups (with Chaim Even-Zohar), Discrete Mathematics 313 (5) (2013), 689–692.

  62. Flat-containing and shift-blocking sets in F2r (with Aart Blokhuis), Moscow Journal of Combinatorics and Number Theory 3 (2) (2013), 3–23.

  63. Solving a±b=2c in the elements of finite sets (with Rom Pinchasi), Acta Arithmetica 163 (2) (2014), 127–140.

  64. Symmetric Kneser's theorem with trios and 3-transform (with David Grynkiewicz), Journal of Combinatorics and Number Theory 7 (3) (2015), 191–212.

  65. Integer sets with identical representation functions (with Yong-Gao Chen), INTEGERS 16 (2016), #A36.

  66. Quadratic residues and difference sets (with Jack Sonn), The Quarterly Journal of Mathematics 68 (1) (2017), 79–95.

  67. Progression-free sets in ℤ4n are exponentially small (with Ernie Croot and Peter Pal Pach), Annals of Mathematics 185 (1) (2017), 331–337.

  68. Stability result for sets with 3A≠ℤ5n, Journal of Combinatorial Theory, Series A 157 (2018), 334–348.

  69. On isoperimetric stability, Discrete Analysis 14 (2018), 11pp.

  70. Small doubling in prime-order groups: from 2.4 to 2.6 (with Ilya Shkredov), Journal of Number Theory 217 (2020), 278–291.

  71. Small doubling in groups with moderate torsion, SIAM Journal of Discrete Mathematics 36 (1) (2022), 315–335.

  72. Sum-full sets are not zero-sum-free (with Janos Nagy and Peter Pach), Linear Algebra and its Applications 625 (2021), 241–247.

  73. The structure of higher sumsets, Proceedings of the American Math. Society 150 (2022), 5165–5177.

  74. Small doubling in cyclic groups, Journal of Number Theory 243 (2023), 561--614.

  75. A nonlinear bound for the number of subsequence sums, European Journal of Combinatorics, to appear.

  76. The popularity gap (with I. Shkredov), Journal of Algebraic Combinatorics 58 (4) (2023), 1155–1172.

  77. Large sum-free sets in ℤ5n, J. Combin. Theory Ser. A, to appear.

  78. Towards 3n-4 in groups of prime order (with O.Serra), Electronic J. Combinatorics 30 (2) (2023), Paper No. 2.48, 10 pp.

  79. Quotient sets in nonabelian groups, Israel Journal of Mathematics, to appear.

  80. Past and future of the capset problem (with Ernie Croot and Peter Pal Pach), submitted.

    C. Popular Papers and Problems

  81. Let us look at diagrams, Kvant 3 (1990), 11–16.

  82. Kvant, Problems M607, M795, M846, M967, M1014, M1029, M1080, M1110, M1120, M1222. Mathematics Magazine, Problem Q767.

    D. Other Papers

  83. Distribution of lattice points on hyperbolic surfaces, Acta Arithmetica 75 (1) (1996), 85–95.

  84. On the distribution of exponential sums (with Sergei Konyagin), INTEGERS: The Electronic Journal of Combinatorial Number Theory 0 (2000), #A01.

  85. Linear equations over Z/pZ and moments of exponential sums, Duke Mathematical Journal 107 (2) (2001), 239–263.

  86. On the maximum value of polynomials with given degree and number of roots (with Sergei Konyagin), Chebyshevskii Sbornik 3 (2)(4) (2003), 156–170.

  87. Character sums in complex half-planes (with Sergei Konyagin), Journal de Théorie des Nombres de Bordeaux 16 (2004), 587–605.

  88. Distribution of points on arcs, INTEGERS: The Electronic Journal of Combinatorial Number Theory 5 (2) (2005), #A11.

  89. More on points and arcs, INTEGERS: The Electronic Journal of Combinatorial Number Theory 7 (2) (2007), #A24.

  90. Projecting difference sets on the positive orthant (with Ron Holzman and Rom Pinchasi), Combinatorics, Probability, and Computing 17 (5) (2008), 681–688.

  91. Approximate convexity and an edge-isoperimetric estimate, Journal of Mathematical Analysis and Applications 416 (2014), 563–574.

  92. Edge-isoperimetric problem for Cayley graphs and generalized Takagi function, SIAM Journal of Discrete Mathematics 29 (4) (2015), 2389–2411.

  93. Discrete norms of a matrix and the converse to the Expander Mixing Lemma, Linear Algebra and its Applications 483 (2015), 158–181.

  94. Minimizing the sum of projections of a finite set (with M. Rudnev), Discrete & Computational Geometry 60 (2) (2018), 493–511.

  95. Uniform distribution and perfect directions in Fp2 Journal of the Uniform Distribution Theory 15 (2) (2020), 93–98.

  96. Uncertainty in finite planes (with A. Biró), Journal of Functional Analysis, 281 (3) (2021), 1–32.

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