Combinatorial proofs for partitions with repeated smallest part
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915287012474880 |
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| author | Chen, Dandan Chen, Rong Zhao, Mengjie |
| author_facet | Chen, Dandan Chen, Rong Zhao, Mengjie |
| contents | Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly $k$ times and the remaining parts are not repeated. They presented several interesting results and posed questions regarding combinatorial proofs for these identities. In this paper, we establish bijections to provide combinatorial proofs for these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial proofs for partitions with repeated smallest part Chen, Dandan Chen, Rong Zhao, Mengjie Combinatorics Number Theory Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly $k$ times and the remaining parts are not repeated. They presented several interesting results and posed questions regarding combinatorial proofs for these identities. In this paper, we establish bijections to provide combinatorial proofs for these results. |
| title | Combinatorial proofs for partitions with repeated smallest part |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2505.05079 |