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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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[5] Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropical
geometry. Math. Z., 259(1):217–230, 2008.
[6] Christian Haase, Gregg Musiker, and Josephine Yu. Linear systems on tropical
curves. Math. Z., 270(3-4):1111–1140, 2012.
[7] Shinsuke Odagiri. Tropical algebraic geometry. Hokkaido Math. J.,
38(4):771–795, 2009.
[8] Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps
in tropical geometry. In Idempotent mathematics and mathematical physics,
volume 377 of Contemp. Math., pages 289–317. Amer. Math. Soc., Providence,
RI, 2005.
[9] David Speyer and Bernd Sturmfels. Tropical mathematics. Math. Mag.,
82(3):163–173, 2009.
[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:[Department of Mathematical Sciences] Theses

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