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論文名稱 Title |
由交換群所定義之拉丁方陣的垂直性 Orthogonality of Latin squares defined by abelian groups |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
33 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2008-07-16 |
繳交日期 Date of Submission |
2008-07-17 |
關鍵字 Keywords |
垂直性、橫截、拉丁方陣 Latin square, transversal, orthogonality |
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統計 Statistics |
本論文已被瀏覽 5704 次,被下載 2025 次 The thesis/dissertation has been browsed 5704 times, has been downloaded 2025 times. |
中文摘要 |
令G為有限交換群,且LG為交換群所定義的拉丁方陣。令k(G)記作為包含LG彼此互相垂直的拉丁方陣個數之最大值。在1948年,Paige證明了若G的2-Sylow子群不是循環群,則LG就有橫截。在論文裡,我們對此定理給了建構性的証明以及討論k(G)的上界與下界。 |
Abstract |
Let G = {g1, …,gn} be a finite abelian group, and let LG = [gij ] be the Latin square defined by gij = gi + gj. Denote by k(G) the largest number of mutually orthogonal system containing LG. In 1948, Paige showed that if the Sylow 2-subgroup of G is not cyclic, then LG has a transversal. In this paper, we give an constructive proof for this theorem and give some upper bound and lower bound for the number k(G). |
目次 Table of Contents |
1.Introduction 1 2.Transveral of Latin square 3 3.Orthogonal Latin square 11 4.Appendix 19 Reference 27 |
參考文獻 References |
[1] N. Alon, Additive Latin transversals, Israel J. Math., 117 (2000) 125-130. [2] M. F. Atiyah; I. G. Macdonald, Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 [3] S. Dasgupta, G. Karolyi, O. Serra and B. Szegedy, Transversals of additive Latin squares, Israel J. Math., 126 (2001) 17-28. [4] I. N. Herstein, Topics in algebra. Second edition. Xerox College Publishing, Lexington, Mass.-Toronto, Ont., 1975. [5] A. Ian, Combinatorial designs and tournaments. Oxford Lecture Series in Mathematics and its Applications, 6. The Clarendon Press, Oxford University Press, New York, 1997. [6] L. J. Paige, Complete mappings of finite groups, Pacific J. Math., 1 (1951), 111-116. [7] L. J. Paige, A note on finite abelian group, Bull. Amer. Math. Soc, (1948) 590-593. |
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