Relations for partitions with distinct even parts except the largest part which is even
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915801693421568 |
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| author | Bardhan, Gaurab Saikia, Nipen |
| author_facet | Bardhan, Gaurab Saikia, Nipen |
| contents | In this paper, we prove some new \(q\)-series identities connecting \(4\)-regular partitions and partitions with distinct even parts with largest part being odd. We also define three new partition functions with distinct even parts except the largest part which is even, and prove identities connecting the three partitions with \(4\)-regular partitions. Moreover, we also offer some congruence for the three newly defined partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relations for partitions with distinct even parts except the largest part which is even Bardhan, Gaurab Saikia, Nipen Number Theory 11P81, 05A17 In this paper, we prove some new \(q\)-series identities connecting \(4\)-regular partitions and partitions with distinct even parts with largest part being odd. We also define three new partition functions with distinct even parts except the largest part which is even, and prove identities connecting the three partitions with \(4\)-regular partitions. Moreover, we also offer some congruence for the three newly defined partitions. |
| title | Relations for partitions with distinct even parts except the largest part which is even |
| topic | Number Theory 11P81, 05A17 |
| url | https://arxiv.org/abs/2602.15454 |