| dc.contributor.advisor | 蔡炎龍 | zh_TW |
| dc.contributor.advisor | Tsai, Yen Lung | en_US |
| dc.contributor.author (作者) | 王珮紋 | zh_TW |
| dc.contributor.author (作者) | Wang, Pei Wen | en_US |
| dc.creator (作者) | 王珮紋 | zh_TW |
| dc.creator (作者) | Wang, Pei Wen | en_US |
| dc.date (日期) | 2013 | en_US |
| dc.date.accessioned | 10-二月-2014 14:55:40 (UTC+8) | - |
| dc.date.available | 10-二月-2014 14:55:40 (UTC+8) | - |
| dc.date.issued (上傳時間) | 10-二月-2014 14:55:40 (UTC+8) | - |
| dc.identifier (其他 識別碼) | G0100972008 | en_US |
| dc.identifier.uri (URI) | https://ah.lib.nccu.edu.tw/item?item_id=71845 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系數學教學碩士在職專班 | zh_TW |
| dc.description (描述) | 100972008 | zh_TW |
| dc.description (描述) | 102 | zh_TW |
| dc.description.abstract (摘要) | 在這篇論文裡，我們研究Baker-Norine的搬硬幣遊戲，並且把這個遊戲應用在離散型的熱帶因子上。特別地，我們去探討這個遊戲與等價熱帶因子之間的關係。最後我們證明了下面的定理:若$D, E$為熱帶曲線$\\Gamma$上的離散型熱帶因子, 而$\\overline{D}$, $\\overline{E}$分別代表因子$D,E$在搬硬幣遊戲時的狀態，因子$D$與$E$等價,若且為若 $\\overline{D}$可經搬硬幣遊戲變成$\\overline{E}$。 | zh_TW |
| dc.description.abstract (摘要) | In this thesis, we study Baker-Norine`s chip-firing game, and apply it to discrete tropical divisors. In particularly, we discuss the relationship between this game and the equivalence of divisors.\n\n Finally, we give a proof of the theorem: \nLet $D$ and $E$ be discrete tropical divisors of tropical curve $\\Gamma$, and let $\\overline{D}$ and $\\overline{E}$ be corresponding configurations of the chip-firing game. \nThe divisors $D$ and $E$ are equivalent if and only if $\\overline{D}$ can be transformed into $\\overline{E}$. | en_US |
| dc.description.tableofcontents | Abstract………i\n中文摘要………ii\n目錄………iv\n\n1 緒論………1\n\n2 熱帶幾何簡介\n2.1熱帶代數的基本介紹………3\n2.2熱帶多項式………5\n2.3熱帶曲線………8\n\n3 圖的因子理論\n3.1 圖形中的因子………15\n3.2 The Chip-Firing Game\n3.2.1 Björner-Lovász-Shor 的發射碎片遊戲………19\n3.2.2 N.Biggs 的發射硬幣遊戲………21\n3.2.3 Baker-Norine 的搬硬幣遊戲………24\n\n4 熱帶幾何的因子理論\n4.1 熱帶幾何中的因子………27\n4.2 搬硬幣遊戲與因子等價的關係………33\n\n5 應用:秩的計算\n5.1 利用搬硬幣遊戲找因子的秩………43\n5.2 利用黎曼-羅赫理論計算因子的秩………46\n\n6 結論………49\n參考文獻………51 | zh_TW |
| dc.format.extent | 1260937 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0100972008 | en_US |
| dc.subject (關鍵詞) | 熱帶曲線 | zh_TW |
| dc.subject (關鍵詞) | 因子 | zh_TW |
| dc.subject (關鍵詞) | tropical curve | en_US |
| dc.subject (關鍵詞) | divisor | en_US |
| dc.subject (關鍵詞) | chip-firing game | en_US |
| dc.title (題名) | 搬硬幣遊戲與離散型熱帶因子等價關係 | zh_TW |
| dc.title (題名) | The Chip-Firing Game and Equivalence of Discrete Tropical Divisors | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] Matthew Baker. Specialization of linear systems from curves to graphs. Algebra\nNumber Theory, 2(6):613–653, 2008. With an appendix by Brian Conrad.\n[2] Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theory\non a finite graph. Adv. Math., 215(2):766–788, 2007.\n[3] N. L. Biggs. Chip-firing and the critical group of a graph. J. Algebraic Combin.,\n9(1):25–45, 1999.\n[4] Anders Björner, László Lovász, and Peter W. Shor. Chip-firing games on\ngraphs. European J. Combin., 12(4):283–291, 1991.\n[5] Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropical\ngeometry. Math. Z., 259(1):217–230, 2008.\n[6] Christian Haase, Gregg Musiker, and Josephine Yu. Linear systems on tropical\ncurves. Math. Z., 270(3-4):1111–1140, 2012.\n[7] Shinsuke Odagiri. Tropical algebraic geometry. Hokkaido Math. J.,\n38(4):771–795, 2009.\n[8] Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps\nin tropical geometry. In Idempotent mathematics and mathematical physics,\nvolume 377 of Contemp. Math., pages 289–317. Amer. Math. Soc., Providence,\nRI, 2005.\n[9] David Speyer and Bernd Sturmfels. Tropical mathematics. Math. Mag.,\n82(3):163–173, 2009.\n[10] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable.\nTaiwanese J. Math., 16(2):691–712, 2012. | zh_TW |
