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英語/数学「Design Theoryデザイン理論」Zhe-Xian Wan/万哲先著 World Scientific Pub発行
        

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  • Listing Date
    :2026年01月19日 12時09分
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    :2026年01月26日 12時09分
  • Auction Number
    :d259144545
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    :Damaged and stained (specify in description)
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洋書・英語/数学「Design Theory/デザイン理論」Zhe-Xian Wan/万哲先著 Highter Education Press/ World Scientific Publishing
Company 2009年発行 目次他9頁+221頁 24×15.9×1.8㎝ 0.51㎏ Hardcover

(裏表紙より) This book deals with the basic subjects of design theory. It begins with balanced incomplete block designs, various constructions of which are described in ample detail. In particular, finite projective and affine planes, ifference sets and Hadamard matrices, as tools to construct balanced incomplete block designs, are included. Orthogonal latin squares are also treated in detail. Zhu's simpler proof of the falsity of Euler's conjecture is included. The construction of some classes of balanced incomplete block designs, such as Steiner triple systems and Kirkman triple systems, are also given. T-designs and partially balanced incomplete block designs (together with association schemes), as generalizations of balanced incomplete block designs, are included. Some coding theory related to Steiner triple systems are clearly explained. The book is written in a lucid style and is algebraic in nature. It can be used as a text or a reference book for graduate students and researchers in combinatorics and applied mathematics. It is also suitable for self-study.
(内容) BIBDs /Symmetric BIBDs /Resolvable BIBDs /Orthogonal Latin Squares /Pairwise Balanced Designs and Group Divisible Designs /Construction of Some Families of BIBDs /t-Designs /Steiner Systems /Association Schemes and PBIBDs
(ウィキペディアより) 組合せ数学(くみあわせすうがく、combinatorics)や組合せ論(くみあわせろん)とは、特定の条件を満たす(普通は有限の)対象からなる集まりを研究する数学の分野。特に問題とされることとして、集まりに入っている対象を数えたり(数え上げ的組合せ論)、いつ条件が満たされるのかを判定し、その条件を満たしている対象を構成したり解析したり(組合せデザインやマトロイド理論)、「最大」「最小」「最適」な対象をみつけたり(極値組合せ論や組合せ最適化)、それらの対象が持ちうる代数的構造をみつけたり(代数的組合せ論)することが挙げられる。……
デザイン理論[編集]:組合せ論のこの分野の単純な結果は序で述べたような集合を構成する問題に答えがあるのはnがq2 + q + 1という形をしたときのみである、というものである。しかし、qが素数べきのときには解が存在し、qが2つの平方数の和であるときは解が存在するかもしれず、そして、それ以外の正整数qに対して解が存在しないということを証明するのはそれ程簡単ではない。この最後の結果はBruck-Chowla-Ryserの定理と呼ばれ、有限体に基づく構成的手法と二次形式の応用を組み合わせて証明された。このような構造が存在するとき、その構造は有限射影平面と呼ばれる。有限幾何と組合せ論が交わっていることを示す例である。

(本の状態) 経年により些か中古感があり、三方に軽ヤケがあり,表紙軽スレがあります。装丁はしっかりしており、中は書き込み等はなく(見落としがありましたらご容赦ください)、概ね並の状態です。本書が中古書であることをご理解の上お買い上げくださいますようお願いいたします。  11301122913
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    Product name: 英語/数学「Design Theoryデザイン理論」Zhe-Xian Wan/万哲先著 World Scientific Pub発行
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