政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/84947

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/84947

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/84947

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/84947

Title:	有限体上的排列多項式之判斷準則的各種證明方法 Various Proofs of PP`s Criteria over Finite Fields
Authors:	解創智 Hsieh, Chuang-Chih
Contributors:	陳永秋解創智 Hsieh, Chuang-Chih
Keywords:	排列多項式有限体 PP Finite fields Permutation polynomials Hermite-Dickson`s Criterion Wan-Turnwald`s Criterion
Date:	2001
Issue Date:	2016-04-15 16:02:49 (UTC+8)
Abstract:	In this paper, we provide a complete survey of the important criteria for permutation polynomials over finite fields, including the classical Hermite-Dickson`s Criterion and the recent Wan-Turnwald`s Criterion. We review the various proofs of these criteria and give new proofs of them. 封面頁證明書致謝詞論文摘要目錄 1 Introduction 2 Hermite-Dickson`s Criterion for Permutation Polynomials 2.1 Dickson`s Proof of Hermite-Dickson`s Criterion 2.2 Carlitz and Lutz`s Proof of Hermite-Dickson`s Criterion 2.3 Lidl and Niederreiter`s Proof of Hermite-Dickson`s Criterion 2.4 Wan and Turnwald`s Proof of Hermite-Dickson`s Criterion 2.5 A New Proof of Hermite-Dickson`s Criterion 3 Wan-Turnwald`s Criterion for Permutation Polynomials 3.1 Wan`s Proof of Wan-Turnwald`s Criterion 3.2 Turnwald`s Proof of Wan-Turnwald`s Criterion 3.3 Generalization for Turnwald`s Proof by Aitken 3.4 A Proof of Wan-Turnwald`s Criterion a la Hermite-Dickson 3.5 An Application to Prove Cohen`s Theorem 4 Equivalent Conditions for Permutation Polynomials 4.1 Fundamental Relations among the Invariants 4.2 New Proofs for Some Inequalities about the Invariants 4.3 Turnwald`s Equivalent Conditions for Permutation Polynomials 5 Further Directions of Research References
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Description:	碩士國立政治大學應用數學系
Source URI:	http://thesis.lib.nccu.edu.tw/record/#A2002001138
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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