Irregularities Of Partitions

de Vera T. Sos

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 Fertöd 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.