Please use this identifier to cite or link to this item:

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
Wang, Pei Wen
Keywords: 熱帶曲線
tropical curve
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
Source URI:
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

Files in This Item:

File SizeFormat
200801.pdf1231KbAdobe PDF103View/Open

All items in 學術集成 are protected by copyright, with all rights reserved.

社群 sharing