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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09819 |
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Table of 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 $ε>0$.