Cyclic sequences of image-subsets with distinct consecutive unions Original Research Article

In this paper, we investigate cyclic sequences which contain as elements all image-subsets of image exactly once such that the unions of any two consecutive image-subsets of this sequences are pairwise distinct. Furthermore, if Y is some prescribed subset of the power set of image, we require that all unions are in Y. In particular, we are interested in the case where Y consists of all subsets of order having the same parity as image. Among others, we show the existence of such cyclic sequences for image and sufficiently large image. This kind of combinatorial problems is motivated from applications in combinatorial group testing. From our results, one obtains error detecting group testing procedures for items having the 2-consecutive positive property.