论文标题
在简单综合体上玩公正的游戏作为皇帝和理论的扩展
Playing impartial games on a simplicial complex as an extension of the emperor sum theory
论文作者
论文摘要
在本文中，我们考虑了简单综合体上的公正游戏。给定的简单络合物的每个顶点都充当公正游戏的位置。每个玩家依次选择一个简单复合体的面，对于该面部每个顶点上的每个位置，玩家都可以进行任意数量的移动。此外，玩家只能为每个顶点上的每个位置而不是在那个脸上做一个动作。我们展示了如何使用P位置长度来表征该游戏的P位置。该结果可以视为皇帝和理论的扩展。尽管皇帝总和仅允许单个组成部分的多次移动，但本研究研究了可以为多个组件做出多个移动的情况，并阐明了皇帝和理论未涵盖的领域。
In this paper, we considered impartial games on a simplicial complex. Each vertex of a given simplicial complex acts as a position of an impartial game. Each player in turn chooses a face of the simplicial complex and, for each position on each vertex of that face, the player can make an arbitrary number of moves. Moreover, the player can make only a single move for each position on each vertex, not on that face. We show how the P-positions of this game can be characterized using the P-position length. This result can be considered an extension of the emperor sum theory. While the emperor sum only allowed multiple moves for a single component, this study examines the case where multiple moves can be made for multiple components, and clarifies areas that the emperor sum theory did not cover.
