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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.09819 |
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| _version_ | 1866909390851801088 |
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| author | Jain, Pranjal Li, Shuo |
| author_facet | Jain, Pranjal Li, Shuo |
| contents | Let $w$ be a finite word over the alphabet $\{0,1\}$. For any natural number $n$, let $s_w(n)$ denote the number of occurrence of $w$ in the binary expansion of $n$ as a scattered subsequence. We study the behavior of the partial sum $\sum_{n=0}^N(-1)^{s_w(n)}$ and characterize several classes of words $w$ satisfying $\sum_{n=0}^N(-1)^{s_w(n)}= O(N^{1-ε})$ for some $ε>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09819 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Partial Sum of Subword-Counting Sequences Jain, Pranjal Li, Shuo Number Theory Combinatorics Let $w$ be a finite word over the alphabet $\{0,1\}$. For any natural number $n$, let $s_w(n)$ denote the number of occurrence of $w$ in the binary expansion of $n$ as a scattered subsequence. We study the behavior of the partial sum $\sum_{n=0}^N(-1)^{s_w(n)}$ and characterize several classes of words $w$ satisfying $\sum_{n=0}^N(-1)^{s_w(n)}= O(N^{1-ε})$ for some $ε>0$. |
| title | On the Partial Sum of Subword-Counting Sequences |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2411.09819 |