可数字母中规定不同数字增长
Prescribed distinct-digit growth in countable alphabets
AI总结：
研究可数字母中不同数字增长的维度规律，发现正线性速率导致维度坍缩，而亚线性速率保持完整维度。
摘要：
研究由全分支仿射可数迭代函数系统生成的数字展开中出现的不同符号数量，其分支权重呈正则变化。确定例外集的Hausdorff维度，其中不同数字计数以正线性速率或规定亚线性速率增长。所得的维度定律表现出明显的相变：施加任何正线性速率会使维度坍缩到仅由尾指数决定的值，而在广泛亚线性增长率下，例外集保持完整的Hausdorff维度。
英文摘要：
The number of distinct symbols appearing in digit expansions generated by full-branch affine countable iterated function systems is studied whose branch weights are regularly varying. The Hausdorff dimensions of the exceptional sets in which the distinct-digit count grows at a positive linear rate or at a prescribed sublinear rate are determined. The resulting dimension laws exhibit a sharp phase transition: imposing any positive linear rate forces the dimension to collapse to a value determined solely by the tail index, whereas under a broad class of sublinear growth rates, the exceptional sets retain full Hausdorff dimension.
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