Titlebook: Ordering Block Designs; Gray Codes, Universa Megan Dewar,Brett Stevens Textbook 2012 Springer Science+Business Media New York 2012 combinat

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Background,signs and design theory concepts used throughout this monograph. The second half of the chapter deals with more advanced concepts, including configurations, Gray codes and universal cycles (Ucycles). We survey a broad range of results in existence and construction of combinatorial Gray codes and Ucy

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Ordering the Blocks of Designs,ign. A listing of the blocks of a design such that there is a minimal change between the content of consecutive blocks is a combinatorial Gray code. Note that the minimal change definition will depend on the design parameters. A listing of points such that the blocks of a design are induced by the c

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Applications,g, reliability testing, group testing and design of specific statistical experiments. The different orderings encountered span the range of possible definitions of orderings. In erasure-correcting codes we see configuration orderings and their initial motivation. In tournament scheduling we see seve

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Results in Configuration Ordering,and similarly review all known results. We conclude the chapter with a look at configuration orderings for graph decompositions other than those represented by balanced incomplete block designs and pairwise balanced designs. .