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arXiv · 2607.00934

On the Extended 1-2-3 Conjecture of Pilz

Philippa Holdridge·Péter Pál Pach
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Abstract

We resolve (for all sufficiently large $n$) a conjecture of Pilz on the symmetric difference $AΔ(2A)Δ\cdotsΔ(nA)$ for finite sets $A\subseteq \mathbb{N}$ of positive integers. We show that this set always has cardinality at least $n$ for large $n$.

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Philippa Holdridge, Péter Pál Pach. 2026-07-01. On the Extended 1-2-3 Conjecture of Pilz. https://arxiv.org/abs/2607.00934

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