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  Cyclic sequences of k-subsets with distinct consecutive unions

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-1B5C-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-1B5D-3
Genre: Journal Article

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 Creators:
Müller, Meinard1, Author              
Jimbo, Masakazu, Author
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 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.

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Language(s): eng - English
 Dates: 2009-03-032008
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 428173
DOI: 10.1016/j.disc.2006.11.062
Other: Local-ID: C125756E0038A185-7DBD696F626CCDEEC125753E0059742E-MuellerJ08_CycSeq_DM
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Title: Discrete Mathematics
Source Genre: Journal
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Pages: - Volume / Issue: 308 (2-3) Sequence Number: - Start / End Page: 457 - 464 Identifier: -