In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If there are no such summands, then the form is indecomposable. The main contribution of this document is the characterization of the indecomposable nimbers and the characterization of the indecomposable numbers. More precisely, a nimber is indecomposable if and only if its size is a power of two, and a number is indecomposable if and only if its absolute value is less than or equal to one.

中文翻译：

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不可分解的组合游戏


在组合博弈论中，短局形式是针对允许两名玩家移动到的所有位置递归定义的。如果一个表单可以表示为两个生日较小的形式的析取和，则该表单是可分解的。如果没有这样的 summand，则 form 是不可分解的。本文档的主要贡献是不可分解 nimbers 的特征和不可分解数字的特征。更准确地说，当且仅当其大小是 2 的幂时，nimber 是不可分解的，并且当且仅当其绝对值小于或等于 1 时，数字是不可分解的。