Discrepancy of Sums of Three Arithmetic Progressions

The set system of all arithmetic progressions on [n] is known to have a discrepancy of order n1/4. We investigate the discrepancy for the set system S3 n formed by all sums of three arithmetic progressions on [n] and show that the discrepancy of S3 n is bounded below by (n1/2). Thus S3 n is one of the few explicit examples of systems with polynomially many sets and a discrepancy this high.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Ales Prívetivý
• Keywords: Arithmetic Progressions, COMBINATORICS 2006, Set System, The Set