Combinatorial Proofs of Some Results of Andrews and El Bachraoui
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913557524774912 |
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| author | Mahanta, Pankaj Jyoti Saikia, Manjil P. |
| author_facet | Mahanta, Pankaj Jyoti Saikia, Manjil P. |
| contents | Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and $4$-regular partitions follow. In this short note, we give combinatorial proofs of these identities. We also prove the counterpart identities for the restricted partitions into distinct odd parts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_15852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial Proofs of Some Results of Andrews and El Bachraoui Mahanta, Pankaj Jyoti Saikia, Manjil P. Combinatorics 05A17, 11P81 Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and $4$-regular partitions follow. In this short note, we give combinatorial proofs of these identities. We also prove the counterpart identities for the restricted partitions into distinct odd parts. |
| title | Combinatorial Proofs of Some Results of Andrews and El Bachraoui |
| topic | Combinatorics 05A17, 11P81 |
| url | https://arxiv.org/abs/2410.15852 |