Parity of parts and excludant statistics in partitions
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 (q), its companion σ*(q) introduced by Ramanujan, and v2(q), a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences.
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