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Title: 一些可分組設計的矩陣建構
Some Matrix Constructions of Group Divisible Designs
Authors: 鄭斯恩
Cheng, Szu En
Contributors: 陳永秋
E. T. Tan
鄭斯恩
Cheng, Szu En
Keywords: 可分組設計
強則圖
斜對稱Hadamard 矩陣
group divisible design
strongly regular graph
skew-symmetric Hadamard matrix
Date: 1993
Issue Date: 2016-04-29 16:32:35 (UTC+8)
Abstract: 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
Reference: [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.
Description: 碩士
國立政治大學
應用數學系
80155011
Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002004241
Data Type: thesis
Appears in Collections:[Department of Mathematical Sciences] Theses

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