This is the binary representation of xi. By Bouton's above-mentioned condition, the numbers xi constitute a "losing combination" if and only if all the sums En= i bim are even. Since the bim are identical with the bi k, all the suns E= 1 bim are even if and only if all the sums 1 biik are even. By Bouton's condition again all the sums J=, bijk are even if and only if each of the sets of numbers aii, where j is fixed, constitutes a "losing combination." From which the conclusion follows: The numbers xi constitute a "losing combination" if and only if each of the sets aii, where j is fixed, constitutes a "losing combination." * C. L. Bouton, Annals of Math., ser. II, vol. 3, 1901, p. 35.
这是xi的二进制表示。根据鲍顿的上述条件，当且仅当所有的和En= i为偶数时，数字xi构成一个“输的组合”。因为b和k是相同的，所以当且仅当所有的和都是偶数时E= 1是偶数。根据Bouton的条件，所有的和J=， bijk都是偶数当且仅当每个集合aii，其中J是固定的，构成一个“损失组合”。由此得出结论:数字xi构成一个“失败的组合”当且仅当每个集合aii(其中j是固定的)构成一个“失败的组合”。C. L. Bouton，《数学年鉴》。,爵士。(二)1901年第三卷，第35页。
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