Integer Partitions With Restricted Distinct Parts
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909740444942336 |
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| author | Drema, Rinchin Saikia, Nipen |
| author_facet | Drema, Rinchin Saikia, Nipen |
| contents | For any positive integers $s$ and $t$, let $Q_{t}^{s}(n)$ denotes the number of partitions of a positive integer $n$ into distinct parts such that no part is congruent to $s$ or $t-s$ modulo $t$. We prove some Ramanujan-type congruences for $Q_{t}^{s}(n)$ for some particular values of $s$ and $t$ by employing $q$-series and theta function identities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integer Partitions With Restricted Distinct Parts Drema, Rinchin Saikia, Nipen Number Theory 11P83, 05A15, 05A17 For any positive integers $s$ and $t$, let $Q_{t}^{s}(n)$ denotes the number of partitions of a positive integer $n$ into distinct parts such that no part is congruent to $s$ or $t-s$ modulo $t$. We prove some Ramanujan-type congruences for $Q_{t}^{s}(n)$ for some particular values of $s$ and $t$ by employing $q$-series and theta function identities. |
| title | Integer Partitions With Restricted Distinct Parts |
| topic | Number Theory 11P83, 05A15, 05A17 |
| url | https://arxiv.org/abs/2508.12739 |