Permutations with a distinct difference property Original Research Article

The topic of this paper arose out of a consideration of Costas sequences, which are used in sonar and radar applications. These sequences have the defining property that all differences of elements the same distance apart, are different. Several infinite families of Costas sequences are known; but there are many existence questions for length ⩾32. In this article, we restrict ourselves to sequences with the weaker property that all adjacent differences are different. We give a recursive construction for these, as well as building several infinite families.