Year: 2024
Type: preprint
Abstract: Based on two involutions and a bijection, we completely determine the difference between the number of $\ell$-regular partitions of $n$ into an even number of parts and into an odd number of parts for all positive integers $n$ and $\ell>1$, which extends two recent results due to Ballantine and Merca. As an application, we provide a combinatorial proof of Hickerson's identity on the number of partitions into an even and odd number of parts.
Source: arXiv (Cornell University)
Author: Liu, Ji-Cai
Institution: Wenzhou University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7668179254
OpenAlex ID: W4399401575