A note on multiset reconstruction from sum and pairwise products
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911087938502656 |
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| author | Li, Stella Jiahui |
| author_facet | Li, Stella Jiahui |
| contents | Ballantine, Beck, and Merca defined a map $\mathrm{pre}_2$, which sends an integer partition $λ= (λ_1, \dots, λ_{\ell})$ to the set $\{λ_iλ_j : 1 \leq i < j \leq \ell\}$ consisting of the pairwise products of parts of $λ$. The same three authors and Sagan conjectured that for each $n$, the map $\mathrm{pre}_2$ is injective on the set of integer partitions of $n$. In this note, we prove their conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on multiset reconstruction from sum and pairwise products Li, Stella Jiahui Combinatorics Ballantine, Beck, and Merca defined a map $\mathrm{pre}_2$, which sends an integer partition $λ= (λ_1, \dots, λ_{\ell})$ to the set $\{λ_iλ_j : 1 \leq i < j \leq \ell\}$ consisting of the pairwise products of parts of $λ$. The same three authors and Sagan conjectured that for each $n$, the map $\mathrm{pre}_2$ is injective on the set of integer partitions of $n$. In this note, we prove their conjecture. |
| title | A note on multiset reconstruction from sum and pairwise products |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.00971 |