AI 中文总结
该研究确定了整数与高斯整数连分数的最优局部收敛准则，分类了两类连分数的极小限制条件，还构造了强于任意有限集合的无限基数规范限制集合。
AI 中文摘要
本研究旨在确定整数连分数与高斯整数连分数系数上可保证收敛的最优局部限制条件。在整数情形中，我们识别出所有涉及长度为2的字的极小限制条件，且该分类等价于Conway–Coxeter quiddity序列中长度为2的极小不可避免字的分类；在高斯整数情形中，我们识别出所有长度为2的可逆极小限制条件。此外，我们还构造了一个无限基数的规范限制集合，其严格强于任意有限限制集合。
英文摘要
The objective of this work is to determine optimal local restrictions on the coefficients of integer and Gaussian integer continued fractions that imply convergence. We identify all minimal restrictions involving words of length two in the integer case, and we identify all reversible minimal restrictions of length two in the Gaussian integer case. In the integer setting, our classification is equivalent to a classification of minimal unavoidable words of length two in Conway--Coxeter quiddity sequences. We also construct a canonical set of restrictions of infinite cardinality that is strictly stronger than every finite set of restrictions.
Comments16 pages, 5 figures
