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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/63704


    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
    Number Theory, 2(6):613–653, 2008. With an appendix by Brian Conrad.
    [2] Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theory
    on a finite graph. Adv. Math., 215(2):766–788, 2007.
    [3] N. L. Biggs. Chip-firing and the critical group of a graph. J. Algebraic Combin.,
    9(1):25–45, 1999.
    [4] Anders Björner, László Lovász, and Peter W. Shor. Chip-firing games on
    graphs. European J. Combin., 12(4):283–291, 1991.
    [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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