Parity considerations in the number of parts
Combinatorics
2026-01-29 v3
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.
Cite
@article{arxiv.2412.20031,
title = {Parity considerations in the number of parts},
author = {Thomas Y. He and H. X. Huang and Y. X. Xie and T. T. Zou},
journal= {arXiv preprint arXiv:2412.20031},
year = {2026}
}