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研究生:侯森棟
研究生(外文):Sheng-Dung Hou
論文名稱:t-結構與t-設計
論文名稱(外文):t-structures and t-designs
指導教授:柯文峰貝德貝德引用關係
指導教授(外文):Wen-Fong KeK.I. Beidar
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:21
中文關鍵詞:結構設計
外文關鍵詞:designstructure
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In this thesis we are going to look at structures and designs.
The subject of design theory has grown out of several branches of
mathematics, and has been increasing influenced in recent years by
developments in other areas. Design theory originated in
statistics (its name reflects its initial use, in experimental
design). Today it has very fruitful connections with group theory,
graph theory, coding theory and geometry. Designs are usually
classified by their parameter sets, by their membership of
infinite families, or according to the type of automorphism group
they admit---or in other ways related to their geometric
properties.
There are many different ways for constructing designs. One of
them is through a more general concept called structures.
By removing repeated blocks from a structure, one can sometimes
obtain designs. It is known that for any positive integers t,
v, and k with t<k≦ v/2, there is a λ such that a
nontrivial uniform t-(v,k,λ) structure exists. By
removing the repeated blocks, one may hope to obtain a design. In
this thesis, we construct some examples of this type. One of
the examples does lead to a design. We hope that these examples
may give insight to the problem of constructing designs with
larger t.
1.Introduction.....................1
2.Basic de finition and theorem ....1
3.Main problem ....................3
3.1.The first example ..............3
3.2.The second example ............6
3.3.The third example ............ 10
4.Appendix ........................13
References ........................15
[1] Erhard Aichinger, Franz Binder, J¨urgen Ecker, Roland Eggetsberger, Peter Mayr and Christof N¨obauer. The Share Package ”SONATA” (System of Nearrings and Their Applications)-
Reference Manual. Institute f. Algebra, Stochastik und wissensbasierte mathematische Systeme, University of Linz, Austria. (http://www.algebra.uni-linz.ac.at/Sonata2)
[2] Th. Beth, D. Jungnickel, and H. Lenz.Design theory vol I. Mannheim, Wien, Z¨urich: Bibliographisches
Institut Wissenschaftsverlag, 1999.
[3] Th. Beth, D. Jungnickel, and H. Lenz.Design theory vol II. Mannheim, Wien, Z¨urich: Bibliographisches
Institut Wissenschaftsverlag, 1999.
[4] B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan and S. M. Watt.
Maple V-Language Reference Manual. New York, Springer-Verlag, 1992.
[5] B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan and S. M. Watt. First
Leaves: A Tutorial Introduction to Maple V. New York, Springer-Verlag, 1992.
[6] D. R. Hughes and F. C. Piper Design Theory. London, Cambridge University Press, 1985.
[7] Martin Sch¨onert, H. U. Besche, T. Breuer, F. Celler, V. Felsch, A, Hulpke, J. Mnich, G.
Pfeier, U. Polis and H. Theiben. GAP-Groups, Algorithms and Programming version 4.2.
Aachen, St Andrews, 2000. (http://www-gap.dcs.st-and.ac.uk/gap)
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