论文标题
超过$ L_5 $有无限的单调游戏
There are infinitely many monotone games over $L_5$
论文作者
论文摘要
塞林格最近在一组部分有序的原子结果集上进行了组合游戏的概念。这些游戏适用于描述在十六进制和其他单调套件上的位置的价值。众所周知，当原子的poset未线性排序时，存在无限的许多独特的单调游戏值，而当原子的poset用4个或更少的元素线性订购时，只有有限的许多此类值。在这篇简短的论文中，我们解决了其余的情况：当原子poset具有5个或更多元素时，有许多不同的单调值。
A notion of combinatorial game over a partially ordered set of atomic outcomes was recently introduced by Selinger. These games are appropriate for describing the value of positions in Hex and other monotone set coloring games. It is already known that there are infinitely many distinct monotone game values when the poset of atoms is not linearly ordered, and that there are only finitely many such values when the poset of atoms is linearly ordered with 4 or fewer elements. In this short paper, we settle the remaining case: when the atom poset has 5 or more elements, there are infinitely many distinct monotone values.
