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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

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 $\overline{E}$.

Identiferoai:union.ndltd.org:CHENGCHI/G0100972008
Creators王珮紋, Wang, Pei Wen
Publisher國立政治大學
Source SetsNational Chengchi University Libraries
Language中文
Detected LanguageEnglish
Typetext
RightsCopyright © nccu library on behalf of the copyright holders

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