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題名 一些可分組設計的矩陣建構
Some Matrix Constructions of Group Divisible Designs作者 鄭斯恩
Cheng, Szu En貢獻者 陳永秋
E. T. Tan
鄭斯恩
Cheng, Szu En關鍵詞 可分組設計
強則圖
斜對稱Hadamard 矩陣
group divisible design
strongly regular graph
skew-symmetric Hadamard matrix日期 1993 上傳時間 29-Apr-2016 16:32:35 (UTC+8) 摘要 在本篇論文中我們使用矩陣來建構可分組設計(GDD), 我們列出了兩種型
In this thesis we use matrices to construct group divisible參考文獻 [1] K. T. Arasu , D. Jungnickel and A. Pott. Symmetric divisible design with k – λ1=1. Discrete Math. , 97:25-38, 1991. [2] K. T. Arasu and A. Pott. Some constructions of group divisible designs with singer groups. Discrete Math. , 97:39-45, 1991. [3] K. T. Arasu, W. H. Haemers , D. Jungnickel and A. Pott. Matrix constructions for divisible designs. Linear Algebra appl. , 153:123-133, 1991. [4] T. Beth, D. Jungnickel and H. Lenz. Design Theory. Cambridge ,Univ., Cam-bridge, 1986. [5] R. C. Bose and W. S. Connor. Combinational properties of group divisible incomplete block design. Ann. Math. Stat. , 23:367-383, 1952. [6] A.E. Brouwer and J.H. Van Lint. Strongly regular graphs and partial geometries. In D. M. Jackson and S. A. Vanstone, editors, Enumeration and Design, pages 475-478. Academic, New York, 1988. [7] W. S. onnor. Some relations among the blocks of symmetric group divisible design. Ann. Math. Stat. , 23:602-609, 1952. [8] W. H. Haemers. Divisible design with r –λ1=1. J. Comb. Theo, Series A, 57:316-319, 1991. [9] M. Jr. Hall. Combinatorial Theory. A Wiley-Interscience publication., New York, 1986. [10] A. Hedayat and W. D. Wallis. Hadamard matrices and theeir applications. Ann. Stat. , 6:1184-1238, 1978. [11] S. Kageyama and T. Tanaka. Some families of group divisible designs. J. Stat. Plann. Interference, 5:231-241, 1981. [12] Z.W. Liu and H.J. Xiao. Construction of group divisible designs by nsing Hadamard matrices. In K. Matusita, editor, Statistical Theory and Data Analysis II, Page 475-478. Elsevier Science Publishers B.V., North-Holland 1988. [13] J. S. Parihar and R. Shrivastaa. Methods of constuction of group divisible designs. J. Stst. Plann. Inference, 18:399-404, 1988. [14] D. Raghavarao.Constructions and Combinatorial Problems in Design of Exper-iments. Wiley, New York, 1971. [15] S. S. Shrikhande. On a two parameter family of balanced incomplete block designs. Sankya, 24:33-40, 1962. [16] A. P. Street and D. J. Street. Combinatorics of Experimental Design. Oxford Univ., New York, 1987. [17] D. J. Street. Some constructions for PBIBDs. J. Stst. Plann. Inference, 10:119-129, 1984. 描述 碩士
國立政治大學
應用數學系
80155011資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002004241 資料類型 thesis dc.contributor.advisor 陳永秋 zh_TW dc.contributor.advisor E. T. Tan en_US dc.contributor.author (Authors) 鄭斯恩 zh_TW dc.contributor.author (Authors) Cheng, Szu En en_US dc.creator (作者) 鄭斯恩 zh_TW dc.creator (作者) Cheng, Szu En en_US dc.date (日期) 1993 en_US dc.date.accessioned 29-Apr-2016 16:32:35 (UTC+8) - dc.date.available 29-Apr-2016 16:32:35 (UTC+8) - dc.date.issued (上傳時間) 29-Apr-2016 16:32:35 (UTC+8) - dc.identifier (Other Identifiers) B2002004241 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/88743 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 80155011 zh_TW dc.description.abstract (摘要) 在本篇論文中我們使用矩陣來建構可分組設計(GDD), 我們列出了兩種型 zh_TW dc.description.abstract (摘要) In this thesis we use matrices to construct group divisible en_US dc.description.tableofcontents Abstract ii 0 Introduction 1 1 Preliminaries 4 1.1 BIBD and PBIBD................................................................................................5 1.1.1 BIBD............................................................................................................5 1.1.2 PBIBD..........................................................................................................7 1.2 GDO.....................................................................................................................8 1.3 Storngly regular graphs(SRG)............................................................................13 1.4 Hadamard matrix................................................................................................15 2 Main Results 21 2.1 Type I : Construction of regular GDDs...............................................................21 2.2 Type II : Constructions of semi-regular and regular GDDs................................29 3 Examples 37 3.1 Type I : Regular GDDs...........................................................................................37 3.2 Type II : Semi-regular and regular GDDs...............................................................40 4 Discussion 44 A Table of GDDs with r—λ1=1 46 B Table of BIBDs with b=4(r-λ) 52 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002004241 en_US dc.subject (關鍵詞) 可分組設計 zh_TW dc.subject (關鍵詞) 強則圖 zh_TW dc.subject (關鍵詞) 斜對稱Hadamard 矩陣 zh_TW dc.subject (關鍵詞) group divisible design en_US dc.subject (關鍵詞) strongly regular graph en_US dc.subject (關鍵詞) skew-symmetric Hadamard matrix en_US dc.title (題名) 一些可分組設計的矩陣建構 zh_TW dc.title (題名) Some Matrix Constructions of Group Divisible Designs en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] K. T. Arasu , D. Jungnickel and A. Pott. Symmetric divisible design with k – λ1=1. Discrete Math. , 97:25-38, 1991. [2] K. T. Arasu and A. Pott. Some constructions of group divisible designs with singer groups. Discrete Math. , 97:39-45, 1991. [3] K. T. Arasu, W. H. Haemers , D. Jungnickel and A. Pott. Matrix constructions for divisible designs. Linear Algebra appl. , 153:123-133, 1991. [4] T. Beth, D. Jungnickel and H. Lenz. Design Theory. Cambridge ,Univ., Cam-bridge, 1986. [5] R. C. Bose and W. S. Connor. Combinational properties of group divisible incomplete block design. Ann. Math. Stat. , 23:367-383, 1952. [6] A.E. Brouwer and J.H. Van Lint. Strongly regular graphs and partial geometries. In D. M. Jackson and S. A. Vanstone, editors, Enumeration and Design, pages 475-478. Academic, New York, 1988. [7] W. S. onnor. Some relations among the blocks of symmetric group divisible design. Ann. Math. Stat. , 23:602-609, 1952. [8] W. H. Haemers. Divisible design with r –λ1=1. J. Comb. Theo, Series A, 57:316-319, 1991. [9] M. Jr. Hall. Combinatorial Theory. A Wiley-Interscience publication., New York, 1986. [10] A. Hedayat and W. D. Wallis. Hadamard matrices and theeir applications. Ann. Stat. , 6:1184-1238, 1978. [11] S. Kageyama and T. Tanaka. Some families of group divisible designs. J. Stat. Plann. Interference, 5:231-241, 1981. [12] Z.W. Liu and H.J. Xiao. Construction of group divisible designs by nsing Hadamard matrices. In K. Matusita, editor, Statistical Theory and Data Analysis II, Page 475-478. Elsevier Science Publishers B.V., North-Holland 1988. [13] J. S. Parihar and R. Shrivastaa. Methods of constuction of group divisible designs. J. Stst. Plann. Inference, 18:399-404, 1988. [14] D. Raghavarao.Constructions and Combinatorial Problems in Design of Exper-iments. Wiley, New York, 1971. [15] S. S. Shrikhande. On a two parameter family of balanced incomplete block designs. Sankya, 24:33-40, 1962. [16] A. P. Street and D. J. Street. Combinatorics of Experimental Design. Oxford Univ., New York, 1987. [17] D. J. Street. Some constructions for PBIBDs. J. Stst. Plann. Inference, 10:119-129, 1984. zh_TW
