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#### Cyclic sequences of k-subsets with distinct consecutive unions

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##### Citation

Müller, M., & Jimbo, M. (2008). Cyclic sequences of k-subsets with distinct consecutive
unions.* Discrete Mathematics,* *308*(2-3), 457-464. doi:10.1016/j.disc.2006.11.062.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-1B5C-5

##### Abstract

In this paper, we investigate cyclic sequences which contain as elements all
k-subsets of {0,1,...,n-1} exactly once such that the unions of any two
consecutive k-subsets of this sequences are pairwise distinct. Furthermore, if
Y is some prescribed subset of the power set of {0,1,...,n-1}, 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 k. Among others, we
show the existence of such cyclic sequences for k=2,3,...,7 and sufficiently
large n. 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.