The problem of the uniform distribution of sequences, first attacked by Hardy, Littlewood and Weyl in the early years of this century, has now become an important part of number theory. This is also true of Ramsey theory in combinatorics, whose origins can be traced back to Schur in the same period. Both concern the distribution of sequences of elements in certain collection of subsets. Quite recently these strands have become interwoven, borne fruit and developed links with such other fields as ergodic theory, geometry, information theory and algorithm theory. This volume is the homogeneous summary of a workshop held at FertAd in Hungary, which brought together people working on various aspects of Ramsey theory on the one hand and on the theory of uniform distribution and related aspects of number theory on the other. The volume consists of 14 papers, 5 on the combinatorial, 5 on the number theoretical aspects and 4 on various generalizations, and a list of unsolved problems. This authoritative state-of-the-art report is addressed to researchers and graduate students.
1. Irregularities of Point Distribution Relative to Convex Polygons.- 2. Balancing Matrices with Line Shifts II.- 3. A Few Remarks on Orientation of Graphs and Ramsey Theory.- 4. On a Conjecture of Roth and Some Related Problems I.- 5. Discrepancy of Sequences in Discrete Spaces.- 6. On the Distribution of Monochromatic Configurations.- 7. Covering Complete Graphs by Monochromatic Paths.- 8. Canonical Partition Behavior of Cantor Spaces.- 9. Extremal Problems for Discrepancy.- 10. Spectral Studies of Automata.- 11. A Diophantine Problem.- 12. A Note on Boolean Dimension of Posets.- 13. Intersection Properties and Extremal Problems for Set Systems.- 14. On an Imbalance Problem in the Theory of Point Distribution.- 15. Problems.