M. Laczkovich

activity

19942026

most citedThe Kakeya problem for circular arcs

6 citations · 11 across the 16 of their papers we have counts for

collaborators

18 papers

math.CO2026

Solution of Erdős Problem 633

Michael Beeson, Miklos Laczkovich, Yan X. Zhang

We classify triangles that can be tiled only into a square number of congruent triangles, settling Erdős Problem 633.

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

Reptile trapezoids

Jin Heo

A geometric figure is a reptile if it can be dissected into at least two similar copies congruent to each other. We prove that if a trapezoid is a reptile and not a parallelogram,…

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.MG2022

Quadrilateral reptiles

Miklos Laczkovich

A polygon $P$ is called a reptile, if it can be decomposed into $k \geq 2$ nonoverlapping and congruent polygons similar to $P$ . We prove that if a cyclic quadrilateral is a reptile,…

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

A superposition theorem of Kolmogorov type for bounded continuous functions

M. Laczkovich

Let $C (R^{n})$ denote the set of real valued continuous functions defined on $R^{n}$ . We prove that for every $n \geq 2$ there are positive numbers $λ_1 , \ldots , λ_…

math.GN2021

Separately polynomial functions

Gergely Kiss, Miklós Laczkovich

It is known that if $f : R^{2} \to R$ is a polynomial in each variable, then $f$ is a polynomial. We present generalizations of this fact, when ${\mathbb R}^2…

math.FA2020

Vector valued polynomials, exponential polynomials and vector valued harmonic analysis

Miklos Laczkovich

Let $G$ be a topological Abelian semigroup with unit, let $E$ be a Banach space, and let $C (G, E)$ denote the set of continuous functions $f : G \to E$ . A function $f \in C (G, E)$ …

math.MG2020

Irregular tilings of regular polygons with similar triangles

M. Laczkovich

We say that a triangle $T$ tiles a polygon $A$ , if $A$ can be dissected into finitely many nonoverlapping triangles similar to $T$ . We show that if $N > 42$ , then there are at most t…

math.CA2018

A characterization of generalized exponential polynomials in terms of decomposable functions

Miklos Laczkovich

Let $G$ be a topological commutative semigroup with unit. We prove that a continuous function $f\colon G\to \cc$ is a generalized exponential polynomial if and only if there is an…

math.RA2018

Derivations and differential operators on rings and fields

Gergely Kiss, Miklós Laczkovich

Let $R$ be an integral domain of characteristic zero. We prove that a function $D : R \to R$ is a derivation of order $n$ if and only if $D$ belongs to the closure of the set of…

math.MG2018★ 6 cited

The Kakeya problem for circular arcs

Kornélia Héra, Miklós Laczkovich

We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.

math.MG2018★ 4 cited

Closed sets with the Kakeya property

Marianna Csörnyei, Kornélia Héra, Miklós Laczkovich

We say that a planar set $A$ has the Kakeya property if there exist two different positions of $A$ such that $A$ can be continuously moved from the first position to the second wit…

math.FA2016

The discrete Pompeiu problem on the plane

Gergely Kiss, Miklós Laczkovich, Csaba Vincze

We say that a finite subset $E$ of the Euclidean plane $R^{2}$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\mathbb{R}^2\to \…

math.MG2014

Magic mirrors, dense diameters, Baire category

Imre Bárány, Miklós Laczkovich

An old result of Zamfirescu says that for most convex curves $C$ in the plane most points in $R^{2}$ lie on infinitely many normals to $C$ , where most is meant in Baire category sens…

math.CA2011

A cardinal number connected to the solvability of systems of difference equations in a given function class

Márton Elekes, Miklós Laczkovich

Let $R^{R}$ denote the set of real valued functions defined on the real line. A map $D : R^{R} \to R^{R}$ is a {\it difference operator}, if there are real numbers $a_i, b_i \ (i=1,…

math.LO1994★ 1 cited

Measurability of functions with approximately continuous vertical sections and measurable horizontal sections

M. Laczkovich, Arnold W. Miller

A function f:R -> R is approximately continuous iff it is continuous in the density topology, i.e., for any ordinary open set U the set E=f^{-1}(U) is measurable and has Lebesgue d…