Gergely Kiss

activity

20112026

most citedOn the discrete Fuglede and Pompeiu problems

22 citations · 77 across the 38 of their papers we have counts for

collaborators

48 papers

math.NT2026

Non-existence of sets with few special directions

Luca Ghidelli, Gergely Kiss, Gábor Somlai

Let $p$ be an odd prime and let $S \subseteq F_{p}^{2}$ have cardinality divisible by $p$ . We prove that, for all sufficiently large primes $p$ , no such set has exactly four spe…

math.GM2026

N-ary quasi-arithmetic means and families without regularity

Gergely Kiss, Ekaterina Shulman

The classical theorems of Kolmogorov--Nagumo--de Finetti and of Aczel--Maksa characterize quasi-arithmetic means from two complementary directions: the former for compatible famili…

math.CO2026

Cylinder type and $p$ -divisible sets in $F_{p}^{3}$

Gergely Kiss, Ádám Markó, Zoltán Lóránt Nagy +1

A set of points $S \subseteq F_{p}^{n}$ is called \emph{ $p$ -divisible} if every affine hyperplane in $F_{p}^{n}$ intersects $S$ in $0 (mod p)$ points. The Strong Cylinder…

math.GM2026

On noncontinuous bisymmetric strictly monotone operations

Gergely Kiss

We construct bisymmetric, partially strictly increasing binary operations on real intervals which are not continuous. This shows that continuity cannot be removed from the classica…

math.NT2025

Lower bounds for mask polynomials with many cyclotomic divisors

Gergely Kiss, Izabella Łaba, Caleb Marshall +1

Given a nonempty set $A \subset N \cup {0}$ , define the mask polynomial $A (X) = \sum_{a \in A} X^{a}$ . Suppose that there are $s_1,\dots,s_k\in\nn\setminus\{1\}$ such that the…

math.MG2025

Invariants and equidecomposability in rings of polygons with sides of given directions

Gergely Kiss, Miklós Laczkovich

We investigate equidecomposability in the ring of polygons with sides restricted to given directions and using only translations. Extending classical results of Dehn and Hadwiger,…

math.CO2024

Functional tilings and the Coven-Meyerowitz tiling conditions

Gergely Kiss, Itay Londner, Máté Matolcsi +1

Coven and Meyerowitz formulated two conditions which have since been conjectured to characterize all finite sets that tile the integers by translation. By periodicity, this conject…

math.CO2024

A lonely weak tile

Gergely Kiss, Itay Londner, Máté Matolcsi +1

The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies \cite{conv}, due to the fact that every spectral set tiles its co…

math.FA2024

Solutions to the discrete Pompeiu problem and to the finite Steinhaus tiling problem

Gergely Kiss, Miklós Laczkovich

Let $K$ be a nonempty finite subset of the Euclidean space $R^{k}$ $(k \geq 2)$ . We prove that if a function $f : R^{k} \to C$ is such that the sum of $f$ o…

math.NT2023

On polynomials of small range sum

Gergely Kiss, Ádám Markó, Zoltán Lóránt Nagy +1

In order to reprove an old result of Rédei's on the number of directions determined by a set of cardinality $p$ in $F_{p}^{2}$ , Somlai proved that the non-constant polynomials…

math.CA2023★ 1 cited

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Thomas Fallon, Gergely Kiss, Azita Mayeli +1

Let $p$ , $q$ , and $r$ be distinct primes such that $p^{2} q^{2} < r$ . We prove that every spectral set in the cyclic group $Z_{p^{2} q^{2} r}$ is a tile. Since the reverse direction is…

math.NT2023

Decompositions of the positive real numbers into disjoint sets closed under addition and multiplication

Gergely Kiss, Gábor Somlai, Tamás Terpai

The main purpose of this paper is to prove that the positive real numbers can be decomposed into finitely many disjoint pieces which are also closed under addition and multiplicati…

math.CA2023

Polynomial equations for additive functions II

Eszter Gselmann, Gergely Kiss

In this sequence of work we investigate polynomial equations of additive functions. We consider the solutions of equation \[ \sum_{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x)^{q_{i}}= 0 \qqua…

math.CO2022

Tiling and weak tiling in $(Z_{p})^{d}$

Gergely Kiss, Dávid Matolcsi, Máté Matolcsi +1

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$ -groups $(Z_{p})^{d}$ , we introduce an averaging pro…

math.CA2022

Sincov's and other functional equations and negative interest rates

Gergely Kiss, Jens Schwaiger

Investigating the future value $F (K, s, t)$ of a capital $K$ invested at date $S$ at date $t$ the "natural" condition $F (K, s, t) \geq K$ has lost its naturality because of the strange…

math.CA2022

Polynomial equations for additive functions I. The inner case

Eszter Gselmann, Gergely Kiss

The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and de…

math.CA2022

A dichotomy result for strictly increasing bisymmetric maps

Pál Burai, Gergely Kiss, Patricia Szokol

In this paper we show some remarkable consequences of the method which proves that every bisymmetric, symmetric, reflexive, strictly monotonic binary map on a proper interval is co…

math.MG2022

Optimal embedded and enclosing isosceles triangles

Aron Ambrus, Monika Csikos, Gergely Kiss +2

Given a triangle $Δ$ , we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of $Δ$ with respect to area and perimeter. This problem wa…

math.CA2022

Isometric rigidity of Wasserstein spaces: the graph metric case

Gergely Kiss, Tamás Titkos

The aim of this paper is to prove that the $p$ -Wasserstein space $W_{p} (X)$ is isometrically rigid for all $p \geq 1$ whenever $X$ is a countable graph metric space. As a co…

math.MG2021★ 2 cited

Nonstandard $n$ -distances based on certain geometric constructions

Gergely Kiss, Jean-Luc Marichal

The concept of $n$ -distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept thro…

math.CO2021

Special directions on the finite affine plane

Gergely Kiss, Gábor Somlai

In this paper we study the number of special directions of sets of cardinality divisible by $p$ on a finite plane of characteristic $p$ , where $p$ is a prime. We show that there is…

math.AC2021

Translation invariant linear spaces of polynomials

Gergely Kiss, Miklós Laczkovich

A set of polynomials $M$ is called a {\it submodule} of $C [x_{1}, \dots, x_{n}]$ if $M$ is a translation invariant linear subspace of $C [x_{1}, \dots, x_{n}]$ . We pre…

math.CA2021

Characterization of quasi-arithmetic means without regularity condition

Pál Burai, Gergely Kiss, Patricia Szokol

In this paper we show that bisymmetry, which is an algebraic property, has a regularity improving feature. More precisely, we prove that every bisymmetric, partially strictly monot…

math.CA2021★ 2 cited

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$

Thomas Fallon, Gergely Kiss, Gábor Somlai

In this paper we study Fuglede's conjecture on the direct product of two cyclic groups. After collecting the known results we prove that Fuglede's conjecture holds on $\mathbb{Z}_{…

Non-existence of sets with few special directions

N-ary quasi-arithmetic means and families without regularity

Cylinder type and p-divisible sets in Fp3​

On noncontinuous bisymmetric strictly monotone operations

Lower bounds for mask polynomials with many cyclotomic divisors

Invariants and equidecomposability in rings of polygons with sides of given directions

Functional tilings and the Coven-Meyerowitz tiling conditions

A lonely weak tile

Solutions to the discrete Pompeiu problem and to the finite Steinhaus tiling problem

On polynomials of small range sum

Spectral Tile Direction in the Group Zp2​×Zq2​×Zr​

Decompositions of the positive real numbers into disjoint sets closed under addition and multiplication

Polynomial equations for additive functions II

Tiling and weak tiling in (Zp​)d

Sincov's and other functional equations and negative interest rates

Polynomial equations for additive functions I. The inner case

A dichotomy result for strictly increasing bisymmetric maps

Optimal embedded and enclosing isosceles triangles

Isometric rigidity of Wasserstein spaces: the graph metric case

Nonstandard n-distances based on certain geometric constructions

Special directions on the finite affine plane

Translation invariant linear spaces of polynomials

Characterization of quasi-arithmetic means without regularity condition

Spectral sets and tiles in Zp2​×Zq2​

Cylinder type and $p$ -divisible sets in $F_{p}^{3}$

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Tiling and weak tiling in $(Z_{p})^{d}$

Nonstandard $n$ -distances based on certain geometric constructions

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$