P. Pach

collaborators

5 papers

math.CO2026

On the Extended 1-2-3 Conjecture of Pilz

Philippa Holdridge, PÃ©ter PÃ¡l Pach

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

math.CO2026

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

JÃ¡nos Nagy, PÃ©ter PÃ¡l 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

PÃ©ter PÃ¡l Pach, Csaba SÃ¡ndor

Let $I ¨ _{k} (N)$ 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 p…

math.NT2025

On the density of Kravitz sets

We show that for a subset $A$ of the cyclic group of prime order $p > 3$ , if the sumset $A + A - 2 A$ is not the whole group, then $∣ A ∣ \leq \frac{2}{7} p$ . Besides combinatorial arguments, we…

math.CO2025

Equidistribution of subset sums

We answer a question of Katona and Makar-Limanov, by showing that in an abelian group of order $2 h$ the $h$ -element subset sums are asymptotically (as $h \to \infty$ ) equidistribute…