Two combinatorial identities are considered. These identities imply that \(\exp \) and \(\log \) are mutually inverse to one another even in the case where the variable is a noncommutative symbol. The proofs are given by enumeration of permutations and flags in a finite set.

中文翻译：

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指数函数与对数函数之间关系的组合证明

考虑两个组合身份。这些标识意味着\（\ exp \）和\（\ log \）彼此相反，即使在变量是非交换符号的情况下。证明是通过对有限集合中的排列和标志进行枚举来给出的。