Parity of parts and excludant statistics in partitions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917341880647680 |
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| author | Mukherjee, Gargi |
| author_facet | Mukherjee, Gargi |
| contents | In this paper, we study restricted excludant statistics depending on its parity in partitions where parts with same parity are distinct. Using $q$-series transformations, we show that generating functions of these partition statistics are related to the quantum modular forms $\s(q)$, its companion $σ^*(q)$ introduced by Ramanujan, and $v_2(q)$, a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity of parts and excludant statistics in partitions Mukherjee, Gargi Number Theory 11P81, 11P82, 11P84 In this paper, we study restricted excludant statistics depending on its parity in partitions where parts with same parity are distinct. Using $q$-series transformations, we show that generating functions of these partition statistics are related to the quantum modular forms $\s(q)$, its companion $σ^*(q)$ introduced by Ramanujan, and $v_2(q)$, a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences. |
| title | Parity of parts and excludant statistics in partitions |
| topic | Number Theory 11P81, 11P82, 11P84 |
| url | https://arxiv.org/abs/2603.13915 |