Overpartitions with parts separated by parity
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912820967243776 |
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| author | Bringmann, Kathrin Cossaboom, Catherine Craig, William |
| author_facet | Bringmann, Kathrin Cossaboom, Catherine Craig, William |
| contents | In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose parts are separated by parity, and we prove various $q$-series identities for these functions. These identities include relations to modular forms, $q$-hypergeometric series, and mock modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Overpartitions with parts separated by parity Bringmann, Kathrin Cossaboom, Catherine Craig, William Number Theory Combinatorics In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose parts are separated by parity, and we prove various $q$-series identities for these functions. These identities include relations to modular forms, $q$-hypergeometric series, and mock modular forms. |
| title | Overpartitions with parts separated by parity |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2507.16769 |