Advertisement

The polynomial method in additive combinatorics

  • Gyula Károlyi
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Abstract

First of all we are going to introduce what we call the polynomial lemma, a simple but very powerful result.

Keywords

Polynomial Method Vandermonde Matrix Euler Theorem Vandermonde Matrix Versus Davenport Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    N. Alon, Additive Latin transversals, Israel J. Math. 117 (2000), 125–130.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    -, Combinatorial Nullstellensatz, Combin. Probab. Comput. 8 (1999), 7–29.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    N. Alon, S. Friedland, and G. Kalai, Every 4-regular graph plus an edge contains a 3-regular subgraph, J. Combin. Theory Ser. B 37 (1984), 92–93.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    N. Alon, M. B. Nathanson, and I. Z. Ruzsa, Adding distinct congruence classes modulo a prime, Amer. Math. Monthly 102 (1995), 250–255.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    N. Alon and Z. Füredi, Covering the cube by affine hyperplanes, European J. Combin. 14 (1993), 79–83.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A. E. Brouwer and A. Schrijver, The blocking number of an affine space, J. Combin. Theory Ser. A 24 (1978), 251–253.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    S. Dasgupta, G. Károlyi, O. Serra, B. Szegedy, Transversals of additive Latin squares, Israel J. Math. 126 (2001), 17–28.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    R. Jamison, Covering finite fields with cosets of subspaces, J. combin. Theory Ser. A 22 (1977), 253–266.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    G. Károlyi, A compactness argument in the additive theory and the polynomial method, Discrete Math. 302 (2005), 124–144.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    H. Snevily, The Cayley addition table of Z n, Amer. Math. Monthly 106 (1999) 584–585.CrossRefMathSciNetGoogle Scholar
  11. [11]
    V. A. Tashkinov, 3-regular subgraphs of 4-regular graphs, Math. Notes 36 (1984), 612–623.MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 2009

Authors and Affiliations

  • Gyula Károlyi
    • 1
  1. 1.Institute of MathematicsEötvös UniversityBudapestHungary

Personalised recommendations