P. Pach

activity

20122023

most citedProgression-free sets in Z_4^n are exponentially small

94 citations · 101 across the 5 of their papers we have counts for

collaborators

9 papers

math.CO2023

Maximal line-free sets in $F_{p}^{n}$

Christian Elsholtz, Jakob Führer, Erik Füredi +4

We study subsets of $F_{p}^{n}$ that do not contain progressions of length $k$ . We denote by $r_{k} (F_{p}^{n})$ the cardinality of such subsets containing a maximal number…

math.NT2022

On sumsets of nonbases of maximum size

Bela Bajnok, Peter Pal Pach

Let $G$ be a finite abelian group. A nonempty subset $A$ in $G$ is called a basis of order $h$ if $h A = G$ ; when $h A \neq = G$ , it is called a nonbasis of order $h$ . Our interest is in…

math.NT2021

Sum-full sets are not zero-sum-free

Vsevolod F. Lev, Janos Nagy, Peter Pal Pach

Let $A$ be a finite, nonempty subset of an abelian group. We show that if every element of $A$ is a sum of two other elements, then $A$ has a nonempty zero-sum subset. That is, a (…

math.NT2018

The number of multiplicative Sidon sets of integers

Hong Liu, Péter Pál Pach

A set $S$ of natural numbers is multiplicative Sidon if the products of all pairs in $S$ are distinct. Erdős in 1938 studied the maximum size of a multiplicative Sidon subset of $\…

math.NT2018★ 6 cited

Monochromatic solutions to $x + y = z^{2}$ in the interval $[N, c N^{4}]$

Péter Pál Pach

Green and Lindqvist proved that for any 2-colouring of $N$ , there are in\-fi\-ni\-tely many monochromatic solutions to $x + y = z^{2}$ . In fact, they showed the existence of a m…

math.CO2018

The step Sidorenko property and non-norming edge-transitive graphs

Daniel Král', Taísa Martins, Péter Pál Pach +1

Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge den…

Maximal line-free sets in Fpn​