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| Title: | 搬硬幣遊戲與離散型熱帶因子等價關係
The Chip-Firing Game and Equivalence of Discrete Tropical Divisors |
| Authors: | 王珮紋
Wang, Pei Wen |
| Contributors: | 蔡炎龍
Tsai, Yen Lung
王珮紋
Wang, Pei Wen |
| Keywords: | 熱帶曲線
因子
tropical curve
divisor
chip-firing game |
| Date: | 2013 |
| Issue Date: | 2014-02-10 14:55:40 (UTC+8) |
| Abstract: | 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$\\overline{E}$。
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.
Finally, we give a proof of the theorem:
Let $D$ 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.
The divisors $D$ and $E$ are equivalent if and only if $\\overline{D}$ can be transformed into $\\overline{E}$. |
| Reference: | [1] Matthew Baker. Specialization of linear systems from curves to graphs. Algebra
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geometry. Math. Z., 259(1):217–230, 2008.
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[10] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable.
Taiwanese J. Math., 16(2):691–712, 2012. |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
100972008
102 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0100972008 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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| 200801.pdf | 1231Kb | Adobe PDF2 | 160 | View/Open |
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