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arXiv · 2508.00971

A note on multiset reconstruction from sum and pairwise products

Stella Jiahui Li
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Abstract

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.

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Stella Jiahui Li. 2025-08-01. A note on multiset reconstruction from sum and pairwise products. https://arxiv.org/abs/2508.00971

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