Signed Partitions and Rogers-Ramanujan type Identities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913834263904256 |
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| author | Alanazi, Abdulaziz M. Munagi, Augustine O. Sills, Andrew V. |
| author_facet | Alanazi, Abdulaziz M. Munagi, Augustine O. Sills, Andrew V. |
| contents | George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561--573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where some of the parts could be negative. Further, Andrews reinterpreted the classical Göllnitz--Gordon partition identities in terms of signed partitions. In the present work, we provide interpretations of the sum sides of Rogers--Ramanujan type identities, including a new signed partition interpretation of the Göllnitz--Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signed Partitions and Rogers-Ramanujan type Identities Alanazi, Abdulaziz M. Munagi, Augustine O. Sills, Andrew V. Combinatorics Number Theory George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561--573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where some of the parts could be negative. Further, Andrews reinterpreted the classical Göllnitz--Gordon partition identities in terms of signed partitions. In the present work, we provide interpretations of the sum sides of Rogers--Ramanujan type identities, including a new signed partition interpretation of the Göllnitz--Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented. |
| title | Signed Partitions and Rogers-Ramanujan type Identities |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2505.08099 |