The emperor sum of combinatorial games is discussed in this study. In this sum, a player moves arbitrarily many times in one component. For every other component, the player moves once at most. The \(\mathcal {P}\)-positions of emperor sums are characterized using a parameter referred to as \(\mathcal {P}\)-position length. An emperor sum is a \(\mathcal {P}\)-position if and only if every component is a \(\mathcal {P}\)-position and the nim-sum of the \(\mathcal {P}\)-position lengths of all components is 0. This is similar to using the nim-sum of \(\mathcal {G}\)-values to characterize the \(\mathcal {P}\)-positions of the disjunctive sum of games.

本研究讨论了组合博弈的皇帝和。在这个总和中，玩家在一个组件中任意移动多次。对于每个其他组件，玩家最多移动一次。皇帝和的\(\mathcal {P}\) -位置使用称为\(\mathcal {P}\) -位置长度的参数来表征。一个皇帝总和为\（\ mathcal {P} \） -位当且仅当每个部件是一个\（\ mathcal {P} \）位和所述的NIM-总和\（\ mathcal {P} \ ) -所有分量的位置长度为 0。这类似于使用\(\mathcal {G}\) -values的 nim-sum来表征\(\mathcal {P}\)- 博弈的分离和的位置。