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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01995 |
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| _version_ | 1866929375958532096 |
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| author | Liu, Ji-Cai |
| author_facet | Liu, Ji-Cai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $\ell$-regular partitions and Hickerson's identity Liu, Ji-Cai Combinatorics 05A17, 05A19 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. |
| title | On $\ell$-regular partitions and Hickerson's identity |
| topic | Combinatorics 05A17, 05A19 |
| url | https://arxiv.org/abs/2406.01995 |