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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. Tanen_US
dc.contributor.author (Authors) 鄭斯恩zh_TW
dc.contributor.author (Authors) Cheng, Szu Enen_US
dc.creator (作者) 鄭斯恩zh_TW
dc.creator (作者) Cheng, Szu Enen_US
dc.date (日期) 1993en_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) B2002004241en_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) 80155011zh_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 divisibleen_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/#B2002004241en_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 designen_US
dc.subject (關鍵詞) strongly regular graphen_US
dc.subject (關鍵詞) skew-symmetric Hadamard matrixen_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 Designsen_US
dc.type (資料類型) thesisen_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