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arXiv · 2603.13915

Parity of parts and excludant statistics in partitions

Gargi Mukherjee
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Abstract

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 $\sigma^*(q)$ introduced by Ramanujan, and $v_2(q)$, a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences.

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Gargi Mukherjee. 2026-03-14. Parity of parts and excludant statistics in partitions. https://arxiv.org/abs/2603.13915

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