arXiv subjects

Y. X. Xie

Publications and source records attributed to Y. X. Xie.

3 recordsLinked to original sources

arXiv2026

Parity considerations in the number of parts

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.

math.CO↗

arXiv2025

Overpartitions with separated overlined parts and non-overlined parts

Recently, Andrews considered the partitions with parts separated by parity, in which parts of a given parity are all smaller than those of the other parity. Inspired from the partitions with parts separated by parity, we investigate the overpartitions with separated overlined parts and non-overlined parts, in which the sizes of overlined parts (resp. non-overlined parts) are greater than or equal to those of non-overlined parts (resp. overlined parts).

math.CO↗

arXiv2025

Six types of separable integer partitions

Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this atricle, we will investigate six types of partitions from the view of the point of separable integer partition classes.

math.CO↗