搬硬幣遊戲與離散型熱帶因子等價關係

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.\n\n Finally, we give a proof of the theorem: \nLet $D$ 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. \nThe divisors $D$ and $E$ are equivalent if and only if $\\overline{D}$ can be transformed into $\\overline{E}$.