Parity of parts and excludant statistics in partitions
Number Theory
2026-03-17 v1
Abstract
In this paper, we study restricted excludant statistics depending on its parity in partitions where parts with same parity are distinct. Using -series transformations, we show that generating functions of these partition statistics are related to the quantum modular forms , its companion introduced by Ramanujan, and , a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences.
Cite
@article{arxiv.2603.13915,
title = {Parity of parts and excludant statistics in partitions},
author = {Gargi Mukherjee},
journal= {arXiv preprint arXiv:2603.13915},
year = {2026}
}