Year: 2026
Type: preprint
Abstract: Recently Dixit, Kumar, and Srivastava investigated what they called Rascoe and non-Rascoe partitions. These are defined to be the set of distinct partitions where the length of the partition is a part of the partition and is not a part respectively. In this note we provide a $q$-series theoretic proof of two identities regarding the generating function for unrestricted Rascoe and non-Rascoe partitions fulfilling a request of Dixit, Kumar, and Srivastava. We also prove a conjecture of Beck relating non-Rascoe partitions and the rank of a partition.
Source: arXiv (Cornell University)
Author: Cuthbertson, Philip
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204880933