000			03628nam a22004815i 4500
001			978-1-4614-4325-4
003			DE-He213
005			20140220083249.0
007			cr nn 008mamaa
008			120828s2012 xxu| s |||| 0|eng d
020			_a9781461443254 _9978-1-4614-4325-4
024	7		_a10.1007/978-1-4614-4325-4 _2doi
050		4	_aQA164-167.2
072		7	_aPBV _2bicssc
072		7	_aMAT036000 _2bisacsh
082	0	4	_a511.6 _223
100	1		_aDewar, Megan. _eauthor.
245	1	0	_aOrdering Block Designs _h[electronic resource] : _bGray Codes, Universal Cycles and Configuration Orderings / _cby Megan Dewar, Brett Stevens.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2012.
300			_aXI, 207 p. 48 illus., 8 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC, _x1613-5237
505	0		_aAbstract -- Acknowledgements -- Introduction -- Background -- Ordering the Blocks of Designs -- Gray Codes and Universal Cycles for Designs -- New Results in Configuration Ordering -- Conclusions and Future Work -- Bibliography -- Index.
520			_aThe study of combinatorial block designs is a vibrant area of combinatorial mathematics with connections to finite geometries, graph theory, coding theory and statistics. The practice of ordering combinatorial objects can trace its roots to bell ringing which originated in 17th century England, but only emerged as a significant modern research area with the work of F. Gray and N. de Bruijn.  These two fascinating areas of mathematics are brought together for the first time in this book. It presents new terminology and concepts which unify existing and recent results from a wide variety of sources. In order to provide a complete introduction and survey, the book begins with background material on combinatorial block designs and combinatorial orderings, including Gray codes — the most common and well-studied combinatorial ordering concept — and universal cycles. The central chapter discusses how ordering concepts can be applied to block designs, with definitions from existing (configuration orderings) and new (Gray codes and universal cycles for designs) research. Two chapters are devoted to a survey of results in the field, including illustrative proofs and examples. The book concludes with a discussion of connections to a broad range of applications in computer science, engineering and statistics. This book will appeal to both graduate students and researchers. Each chapter contains worked examples and proofs, complete reference lists, exercises and a list of conjectures and open problems. Practitioners will also find the book appealing for its accessible, self-contained introduction to the mathematics behind the applications.
650		0	_aMathematics.
650		0	_aComputational complexity.
650		0	_aCombinatorics.
650	1	4	_aMathematics.
650	2	4	_aCombinatorics.
650	2	4	_aMathematics, general.
650	2	4	_aDiscrete Mathematics in Computer Science.
700	1		_aStevens, Brett. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461443247
830		0	_aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC, _x1613-5237
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-4325-4
912			_aZDB-2-SMA
999			_c101496 _d101496