We show that the class of Kalmár elementary functions can be inductively generated from the addition, the integer remainder, and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints.

翻译：我们证明了卡尔玛初等函数类可由加法、整数取余运算以及二进制指数运算归纳生成，从而改进了马尔琴科夫和马赞蒂先前的研究结果。同时，我们证明了由这三种运算定义的替换基具有最小性。此外，我们还讨论了在元数约束下的替代替换基。