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:  Matthew Baker. Specialization of linear systems from curves to graphs. AlgebraNumber Theory, 2(6):613–653, 2008. With an appendix by Brian Conrad. Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theoryon a finite graph. Adv. Math., 215(2):766–788, 2007. N. L. Biggs. Chip-firing and the critical group of a graph. J. Algebraic Combin.,9(1):25–45, 1999. Anders Björner, László Lovász, and Peter W. Shor. Chip-firing games ongraphs. European J. Combin., 12(4):283–291, 1991. Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropicalgeometry. Math. Z., 259(1):217–230, 2008. Christian Haase, Gregg Musiker, and Josephine Yu. Linear systems on tropicalcurves. Math. Z., 270(3-4):1111–1140, 2012. Shinsuke Odagiri. Tropical algebraic geometry. Hokkaido Math. J.,38(4):771–795, 2009. 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. David Speyer and Bernd Sturmfels. Tropical mathematics. Math. Mag.,82(3):163–173, 2009. 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

Files in This Item:

File SizeFormat