Parity considerations in the number of parts

2024/12/28 by Thomas Y. He, Hongxia Huang, He, Thomas Y. +4
Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Manufacturing Process and Optimization

paper · pdf · doi:10.48550/arxiv.2412.20031

openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Related

• Overpartitions with separated overlined parts and non-overlined parts
• Separable overpartition classes and the r-chain excludant sizes of an overpartition
• Three types of the minimal excludant size of an overpartition
• Perfect Overpartitions and Factorization of Integers
• A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions