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arXiv · 2412.20031

Parity considerations in the number of parts

Thomas Y. He·H. X. Huang·Y. X. Xie·T. T. Zou
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Abstract

Recently, Chen, He, Hu and Xie considered the parity of the number of non-overlined (resp. overlined) parts of size greater than or equal to the size of the smallest overlined (resp. non-overlined) part in an overpartition. In this article, we investigate the parity of the number of non-overlined (resp. overlined) parts of size less than or equal to the size of the largest overlined (resp. non-overlined) part in an overpartition. We also study the parity of the number of even parts greater than the smallest odd part in a partition.

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Thomas Y. He, H. X. Huang, Y. X. Xie, T. T. Zou. 2026-01-28. Parity considerations in the number of parts. https://arxiv.org/abs/2412.20031

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