Prescribed distinct-digit growth in countable alphabets
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917269817262080 |
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| author | Lee, Ying Wai |
| author_facet | Lee, Ying Wai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prescribed distinct-digit growth in countable alphabets Lee, Ying Wai Dynamical Systems Number Theory Probability 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. |
| title | Prescribed distinct-digit growth in countable alphabets |
| topic | Dynamical Systems Number Theory Probability |
| url | https://arxiv.org/abs/2602.11458 |