Arithmetic properties of partition functions introduced by Pushpa and Vasuki
Number Theory
2025-09-11 v1 Combinatorics
Abstract
In this short note, we prove several infinite family of congruences for some restricted partitions introduced by Pushpa and Vasuki (2022) (thereby, also proving a conjecture of Dasappa et. al. (2023)). We also prove some isolated congruences which seem to have been missed by earlier authors. Our proof techniques uses both elementary means as well as the theory of modular forms.
Cite
@article{arxiv.2509.08801,
title = {Arithmetic properties of partition functions introduced by Pushpa and Vasuki},
author = {Hemjyoti Nath and Manjil P. Saikia},
journal= {arXiv preprint arXiv:2509.08801},
year = {2025}
}