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A requested analytic proof of an identity of Dixit, Kumar, and Srivastava
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.
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BibTeX
@misc{cuthbertson2026requested,
title = {{A requested analytic proof of an identity of Dixit, Kumar, and Srivastava}},
author = {Philip Cuthbertson},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30180},
eprint = {2608.30180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30180},
}
RIS
TY - UNPB
TI - A requested analytic proof of an identity of Dixit, Kumar, and Srivastava
AU - Philip Cuthbertson
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30180
UR - https://arxiv.org/abs/2608.30180
AB - 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.
ER -