Recurrence relations for harmonic and derangement numbers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915492383424512 |
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| author | Kim, Taekyun Kim, Dae san Kwon, Jongkyum Hwang, Kyo-Shin |
| author_facet | Kim, Taekyun Kim, Dae san Kwon, Jongkyum Hwang, Kyo-Shin |
| contents | We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the underlying structure of these numbers but also highlight the effectiveness of elementary techniques in discovering new mathematical properties. The findings have potential applications in various fields where these numbers appear, including combinatorics, probability, and computer science. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recurrence relations for harmonic and derangement numbers Kim, Taekyun Kim, Dae san Kwon, Jongkyum Hwang, Kyo-Shin Number Theory 11B83 We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the underlying structure of these numbers but also highlight the effectiveness of elementary techniques in discovering new mathematical properties. The findings have potential applications in various fields where these numbers appear, including combinatorics, probability, and computer science. |
| title | Recurrence relations for harmonic and derangement numbers |
| topic | Number Theory 11B83 |
| url | https://arxiv.org/abs/2509.10404 |