Zeckendorf展开式与基phi展开式的数字和函数
The sum of digits functions of the Zeckendorf and the base phi expansions
摘要：
我们考虑的数字和函数的基φ，并为Zeckendorf展开的自然数。对于这两个数字和功能，我们提出了无限字母表上的态射，这些功能被视为无限的话是字母到字母的投影这些态射的不动点。我们用广义Beatty序列或广义Beatty序列的并刻画了这两个函数的一阶差;用形态序列刻画了这两个函数的一阶差。
英文摘要：
We consider the sum of digits functions for both base phi, and for the Zeckendorf expansion of the natural numbers. For both sum of digits functions we present morphisms on infinite alphabets such that these functions viewed as infinite words are letter-to-letter projections of fixed points of these morphisms. We characterize the first differences of both functions a) with generalized Beatty sequences, or unions of generalized Beatty sequences, and b) with morphic sequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
