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https://ah.lib.nccu.edu.tw/handle/140.119/84947| 題名: | 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 |
作者: | 解創智 Hsieh, Chuang-Chih |
貢獻者: | 陳永秋 解創智 Hsieh, Chuang-Chih |
關鍵詞: | 排列多項式 有限体 PP Finite fields Permutation polynomials Hermite-Dickson`s Criterion Wan-Turnwald`s Criterion |
日期: | 2001 | 上傳時間: | 15-Apr-2016 | 摘要: | 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\r\n證明書\r\n致謝詞\r\n論文摘要\r\n目錄\r\n1 Introduction\r\n2 Hermite-Dickson`s Criterion for Permutation Polynomials\r\n2.1 Dickson`s Proof of Hermite-Dickson`s Criterion\r\n2.2 Carlitz and Lutz`s Proof of Hermite-Dickson`s Criterion\r\n2.3 Lidl and Niederreiter`s Proof of Hermite-Dickson`s Criterion\r\n2.4 Wan and Turnwald`s Proof of Hermite-Dickson`s Criterion\r\n2.5 A New Proof of Hermite-Dickson`s Criterion\r\n3 Wan-Turnwald`s Criterion for Permutation Polynomials\r\n3.1 Wan`s Proof of Wan-Turnwald`s Criterion\r\n3.2 Turnwald`s Proof of Wan-Turnwald`s Criterion\r\n3.3 Generalization for Turnwald`s Proof by Aitken\r\n3.4 A Proof of Wan-Turnwald`s Criterion a la Hermite-Dickson\r\n3.5 An Application to Prove Cohen`s Theorem\r\n4 Equivalent Conditions for Permutation Polynomials\r\n4.1 Fundamental Relations among the Invariants\r\n4.2 New Proofs for Some Inequalities about the Invariants\r\n4.3 Turnwald`s Equivalent Conditions for Permutation Polynomials\r\n5 Further Directions of Research\r\nReferences |
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資料來源: | http://thesis.lib.nccu.edu.tw/record/#A2002001138 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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