Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917801877307392 |
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| author | Fu, Shishuo Li, Haijun |
| author_facet | Fu, Shishuo Li, Haijun |
| contents | Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a double sum $q$-series. Equipped with such a combinatorial set-up, we investigate a handful of double sum identities appeared in recent works of Cao-Wang, Wang-Wang, Wei-Yu-Ruan, Andrews-Uncu, Chern, and Wang, finding partition theoretical interpretations to all of these identities, and in most cases supplying Franklin-type involutive proofs. This approach dates back more than a century to P. A. MacMahon's interpretations of the celebrated Rogers-Ramanujan identities, and has been further developed by Kurşungöz in the last decade. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities Fu, Shishuo Li, Haijun Combinatorics 11P84, 05A19, 05A15 Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a double sum $q$-series. Equipped with such a combinatorial set-up, we investigate a handful of double sum identities appeared in recent works of Cao-Wang, Wang-Wang, Wei-Yu-Ruan, Andrews-Uncu, Chern, and Wang, finding partition theoretical interpretations to all of these identities, and in most cases supplying Franklin-type involutive proofs. This approach dates back more than a century to P. A. MacMahon's interpretations of the celebrated Rogers-Ramanujan identities, and has been further developed by Kurşungöz in the last decade. |
| title | Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities |
| topic | Combinatorics 11P84, 05A19, 05A15 |
| url | https://arxiv.org/abs/2410.09777 |