Uniform perfect systems of sets of iterated differences of size 41 Original Research Article

A general problem raised by the work of Kreweras and Loeb concerns the existence of partitions of runs of consecutive integers into sets, known as sets of iterated differences, the s(s + 1)/2 elements of which can be expressed as certain linear combinations of s integer valued parameters. In this paper we study the case of four parameters. By examining properties already present in examples with only a single set, we build up the rudiments of an arithmetic of these partitions comparable to that for perfect systems of difference sets and complete permutations.