Optimal Littlewood-Offord Inequalities in Groups

This is a preview of subscription content, access via your institution.


  1. [1]

    A. Benjamin, B. Chen and K. Kindred: Sums of Evenly Spaced Binomial Coefficients, Mathematics Magazine 83 (2010), 370–373.

    Article  Google Scholar 

  2. [2]

    B. Bollobás: Combinatorics, Cambridge University Press, Cambridge, 1986, Set systems, hypergraphs, families of vectors and combinatorial probability.

    Google Scholar 

  3. [3]

    P. Diaconis: Random walks on groups: characters and geometry, London Mathematical Society Lecture Note Series, vol. 1, 120-142, Cambridge University Press, 2003.

    Google Scholar 

  4. [4]

    D. Dzindzalieta, T. Juškevičius and M. Šileikis: Optimal probability inequalities for random walks related to problems in extremal combinatorics, SIAM J. Discrete Math. 26 (2012), 828–837.

    MathSciNet  Article  Google Scholar 

  5. [5]

    P. Erdős: On a lemma of Littlewood and Offord, Bull. Amer. Math. Soc. 51 (1945), 898–902.

    MathSciNet  Article  Google Scholar 

  6. [6]

    J. R. Griggs: On the distribution of sums of residues, Bull. Amer. Math. Soc. (N.S.) 28 (1993), 329–333.

    MathSciNet  Article  Google Scholar 

  7. [7]

    D. J. Kleitman: On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors, Advances in Math. 5 (1970), 155–157.

    MathSciNet  Article  Google Scholar 

  8. [8]

    D. A. Levin, Y. Peres and E. L. Wilmer: Markov chains and mixing times, American Mathematical Society, 2006.

    Google Scholar 

  9. [9]

    J. E. Littlewood and A. C. Offord: On the number of real roots of a random algebraic equation. III, Rec. Math. [Mat. Sbornik] N.S. 12 (1943), 277–286.

    MathSciNet  MATH  Google Scholar 

  10. [10]

    P. H. Tiep and V. H. Vu: Non-abelian Littlewood-Offord inequalities, Advances in Mathematics 302 (2016), 1233–1250.

    MathSciNet  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Tomas Juškevičius.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Juškevičius, T., Šemetulskis, G. Optimal Littlewood-Offord Inequalities in Groups. Combinatorica 39, 911–921 (2019). https://doi.org/10.1007/s00493-018-3845-7

Download citation

Mathematics Subject Classification (2010)

  • 05D40
  • 60B15