一类边权三结点循环图上的Eriksson数对策
Eriksson's numbers game on certain edge-weighted three-node cyclic graphs
摘要：
数字博弈是在有限的单图上进行的单人博弈，图的边被赋予一定的“振幅”，节点的初始分配为实数。游戏的移动以一定的方式使用幅度连续地变换节点处的数字。这个博弈及其与Coxeter/外尔群理论和李理论的相互作用已经被许多作者研究过。在Eriksson的基础上，我们允许图边的幅值为某些实数.在这种图形上玩的游戏是“电子游戏”。我们证明，对于某些这样的三节点循环图，任何数字游戏将分歧时，发挥从非负实数不全为零的初始分配。这一结果是一个关键步骤，在Dynkin图分类（其他地方获得）的所有电子游戏图，满足一定的有限性要求。
英文摘要：
The numbers game is a one-player game played on a finite simple graph with certain ``amplitudes'' assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. This game and its interactions with Coxeter/Weyl group theory and Lie theory have been studied by many authors. Following Eriksson, we allow the amplitudes on graph edges to be certain real numbers. Games played on such graphs are ``E-games.'' We show that for certain such three-node cyclic graphs, any numbers game will diverge when played from an initial assignment of nonnegative real numbers not all zero. This result is a key step in a Dynkin diagram classification (obtained elsewhere) of all E-game graphs which meet a certain finiteness requirement.
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