Asymptotics for moments of the minimal partition excludant in congruence classes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916851617890304 |
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| author | Chern, Shane Xia, Ernest X. W. |
| author_facet | Chern, Shane Xia, Ernest X. W. |
| contents | The minimal excludant statistic, which denotes the smallest positive integer that is not a part of an integer partition, has received great interest in recent years. In this paper, we move on to the smallest positive integer whose frequency is less than a given number. We establish an asymptotic formula for the moments of such generalized minimal excludants that fall in a specific congruence class. In particular, our estimation reveals that the moments associated with a fixed modulus are asymptotically ``equal''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics for moments of the minimal partition excludant in congruence classes Chern, Shane Xia, Ernest X. W. Number Theory Combinatorics The minimal excludant statistic, which denotes the smallest positive integer that is not a part of an integer partition, has received great interest in recent years. In this paper, we move on to the smallest positive integer whose frequency is less than a given number. We establish an asymptotic formula for the moments of such generalized minimal excludants that fall in a specific congruence class. In particular, our estimation reveals that the moments associated with a fixed modulus are asymptotically ``equal''. |
| title | Asymptotics for moments of the minimal partition excludant in congruence classes |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2507.14431 |