Please use this identifier to cite or link to this item: https://ah.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 curvedivisorchip-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. AlgebraNumber Theory, 2(6):613–653, 2008. With an appendix by Brian Conrad.[2] Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theoryon 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 ongraphs. European J. Combin., 12(4):283–291, 1991.[5] Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropicalgeometry. Math. Z., 259(1):217–230, 2008.[6] Christian Haase, Gregg Musiker, and Josephine Yu. Linear systems on tropicalcurves. 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 stepsin 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100972008102 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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