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 greater-or-equal to 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.
Field of Research
010104 Combinatorics and Discrete Mathematics (excl Physical Combinatorics)
Socio Economic Objective
970101 Expanding Knowledge in the Mathematical Sciences
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