整数群上增长函数的次可乘性与增长率
Submultiplication and Growth Rate of Growth Functions on the Integer Group
DOI: 10.12677/AAM.2025.144218, PDF,   
作者: 卢斯悦：南京航空航天大学数学学院，江苏 南京
关键词: 整数群；增长函数；次可乘；增长率；Integer Group； Growth Function； Submultiplication； Growth Rate
摘要: 本文给出了整数群 Z 上一个真的长度函数，并证明了这个长度函数诱导的增长函数不是次可乘的， 但却满足一个一般的次可乘不等式。同时计算出了该增长函数的增长率是欧拉数 e。
Abstract: We give a proper length function on the integer group Z, and demonstrate that its induced growth function is not submultiplicative, but satisfies a general submultiplica- tive inequality. We also show that the growth rate of this growth function is Euler’s number e.
文章引用：卢斯悦. 整数群上增长函数的次可乘性与增长率[J]. 应用数学进展, 2025, 14(4): 944-953. https://doi.org/10.12677/AAM.2025.144218

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