论文标题
凸几何的公正成就游戏
Impartial Achievement Games on Convex Geometries
论文作者
论文摘要
我们研究了一个游戏，其中两个玩家轮流选择了凸几何的点，直到共同选择的点的凸关闭包含给定获胜的所有点为止。游戏的获胜者是最后能够移动的球员。我们为这些游戏开发了一个结构理论，并使用它来确定几类凸几何形状的NIM数字，包括一维仿射几何，树木的顶点几何以及具有胜利集的游戏。
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to move. We develop a structure theory for these games and use it to determine the nim number for several classes of convex geometries, including one-dimensional affine geometries, vertex geometries of trees, and games with a winning set consisting of extreme points.
