Ordering block designs : gray codes, universal cycles and configuration orderings
著者
書誌事項
Ordering block designs : gray codes, universal cycles and configuration orderings
(CMS books in mathematics)(Canadian mathematical society = Société mathématique du Canada)
Springer, c2012
大学図書館所蔵 全5件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical reference and index
内容説明・目次
内容説明
The 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.
目次
- Introduction.- Background.- Ordering the Blocks of Designs.- Results in Configuration Ordering.- Results in Gray Codes and Universal Cycles for Designs.-Applications.- Bibliography.- Index.
「Nielsen BookData」 より