P'eter P'al Pach

activity

20162022

most citedSets avoiding six-term arithmetic progressions in

Z_{6}^{n}

are exponentially small

1 citations · 2 across the 6 of their papers we have counts for

collaborators

10 papers

math.CO2022

Towards characterizing the 2-Ramsey equations of the form $a x + b y = p (z)$

Zsolt Baja, Dániel Dobák, Benedek Kovács +2

In this paper, we study a Ramsey-type problem for equations of the form $a x + b y = p (z)$ . We show that if certain technical assumptions hold, then any 2-colouring of the positive integ…

math.CO2021★ 1 cited

The Alon-Jaeger-Tarsi conjecture via group ring identities

János Nagy, Péter Pál Pach

In this paper we resolve the Alon-Jaeger-Tarsi conjecture for sufficiently large primes. Namely, we show that for any finite field $F$ of size $61 < ∣ F ∣ \neq = 79$ and a…

math.CO2020

Avoiding right angles and certain Hamming distances

Balázs Bursics, Dávid Matolcsi, Péter Pál Pach +1

In this paper we show that the largest possible size of a subset of $F_{q}^{n}$ avoiding right angles, that is, distinct vectors $x, y, z$ such that $x - z$ and $y - z$ are perpendi…

math.CO2020★ 1 cited

Sets avoiding six-term arithmetic progressions in $Z_{6}^{n}$ are exponentially small

Péter Pál Pach, Richárd Palincza

We show that sets avoiding 6-term arithmetic progressions in $Z_{6}^{n}$ have size at most $5.70 9^{n}$ . It is also pointed out that the "product construction" does not work in t…

math.CO2020

The counting version of a problem of Erdős

Péter Pál Pach, Richárd Palincza

A set $A$ of natural numbers possesses property $P_{h}$ , if there are no distinct elements $a_{0}, a_{1}, \dots, a_{h} \in A$ with $a_{0}$ dividing the product $a_{1} a_{2} \dots a_{h}$ . Erdő…

math.CO2019

Caps and progression-free sets in $Z_{m}^{n}$

Christian Elsholtz, Péter Pál Pach

We study progression-free sets in the abelian groups $G = (Z_{m}^{n}, +)$ . Let $r_{k} (Z_{m}^{n})$ denote the maximal size of a set $S \subset Z_{m}^{n}$ that does not con…