Irregularities of Partitions

1. Front Matter

   Pages i-vii

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2. Irregularities of Point Distribution Relative to Convex Polygons

   • J. Beck, W. W. L. Chen

   Pages 1-22

3. Balancing Matrices with Line Shifts II

   • J. Beck, J. Spencer

   Pages 23-37

4. A Few Remarks on Orientation of Graphs and Ramsey Theory

   • M. Cochand, P. Duchet

   Pages 39-46

5. On a Conjecture of Roth and Some Related Problems I

   • P. Erdős, A. Sárközy, V. T. Sós

   Pages 47-59

6. Discrepancy of Sequences in Discrete Spaces

   • Ph. Flajolet, P. Kirschenhofer, R. F. Tichy

   Pages 61-70

7. On the Distribution of Monochromatic Configurations

   • P. Frankl, R. L. Graham, V. Rödl

   Pages 71-87

8. Covering Complete Graphs by Monochromatic Paths

   • A. Gyárfás

   Pages 89-91

9. Canonical Partition Behaviour of Cantor Spaces

   • Hanno Lefmann

   Pages 93-105

10. Extremal Problems for Discrepancy

    • L. Lovász, K. Vesztergombi

    Pages 107-113

11. Spectral Studies of Automata

    • J. H. Loxton

    Pages 115-128

12. A Diophantine Problem

    • M. Mendes France

    Pages 129-135

13. A Note on Boolean Dimension of Posets

    • J. Nešetřil, P. Pudlák

    Pages 137-140

14. Intersection Properties and Extremal Problems for Set Systems

    • Zs. Tuza

    Pages 141-151

15. On an Imbalance Problem in the Theory of Point Distribution

    • G. Wagner

    Pages 153-160

16. Problems

    • Gábor Halász, Vera T. Sós

    Pages 161-165

17. Back Matter

    Pages 167-168

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The problem of uniform distribution of sequences initiated by Hardy, Little­ wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey­ theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear­ ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec­ ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.

• Combinatorics
• Partition
• Ramsey theory
• algorithms
• graphs
• number theory

• Department of Analysis, Eötvös Loránd University, Budapest VIII, Hungary

  Gábor Halász

• Mathematical Institute of the Hungarian Academy of Sciences, Budapest V, Hungary

  Vera T. Sós

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