A refined view of a curious identity for partitions into odd parts with designated summands
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918036460535808 |
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| author | Fu, Shishuo Sellers, James |
| author_facet | Fu, Shishuo Sellers, James |
| contents | In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are constructed by taking unrestricted integer partitions and designating exactly one of each occurrence of a part. In the same work, they also considered the restricted partitions with designated summands wherein all parts must be odd, and they denoted the corresponding function by $\mathrm{PDO}(n)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_21111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A refined view of a curious identity for partitions into odd parts with designated summands Fu, Shishuo Sellers, James Combinatorics Discrete Mathematics 11P84, 05A17, 05A15, 33B10 In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are constructed by taking unrestricted integer partitions and designating exactly one of each occurrence of a part. In the same work, they also considered the restricted partitions with designated summands wherein all parts must be odd, and they denoted the corresponding function by $\mathrm{PDO}(n)$. |
| title | A refined view of a curious identity for partitions into odd parts with designated summands |
| topic | Combinatorics Discrete Mathematics 11P84, 05A17, 05A15, 33B10 |
| url | https://arxiv.org/abs/2505.21111 |