P. Pach

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20242026

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math.CO2026

On the Extended 1-2-3 Conjecture of Pilz

Philippa Holdridge, Péter Pál Pach

We resolve (for all sufficiently large $n$ ) a conjecture of Pilz on the symmetric difference $A Δ (2 A) Δ \dots Δ (n A)$ for finite sets $A \subseteq N$ of positive integers. We s…

math.CO2026

On a group ring identity related to the Alon-Jaeger-Tarsi conjecture

János Nagy, Péter Pál Pach

In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.

math.CO2026

Product representations of perfect powers

Péter Pál Pach, Csaba Sándor

Let $ρ_{k} (N)$ denote the maximum size of a set $A \subseteq {1, 2, \dots, N}$ such that no product of $k$ distinct elements of $A$ is a perfect $d$ -th power. In this short note, we pr…