5 citations · 11 across the 7 of their papers we have counts for
15 papers
On monohedral tilings of a regular polygon
Bushra Basit, Zsolt Lángi
A tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J. Combin. Theory Ser. A 66: 40-52, 1994) characterized the monohedral…
Morse-Smale complexes on convex polyhedra
Balázs Ludmány, Zsolt Lángi, Gábor Domokos
Motivated by applications in geomorphology, the aim of this paper is to extend Morse-Smale theory from smooth functions to the radial distance function (measured from an internal p…
An isoperimetric problem for three-dimensional parallelohedra
Zsolt Lángi
The aim of this note is to investigate isoperimetric-type problems for -dimensional parallelohedra; that is, for convex polyhedra whose translates tile the -dimensional Eucli…
On generalized Minkowski arrangements
Máté Kadlicskó, Zsolt Lángi
The concept of a Minkowski arrangement was introduced by Fejes Tóth in 1965 as a family of centrally symmetric convex bodies with the property that no member of the family contains…
Extremal convex polygons inscribed in a given convex polygon
Csenge Lili Ködmön, Zsolt Lángi
A convex polygon is inscribed in a convex polygon if every side of contains at least one vertex of . We present algorithms for finding a minimum area and a minimum p…
On the convex hull and homothetic convex hull functions of a convex body
Ákos G. Horváth, Zsolt Lángi
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body in Euclidean -space, defined as the volume…
A solution to some problems of Conway and Guy on monostable polyhedra
Zsolt Lángi
A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding mo…
On -diametral point configurations in Minkowski spaces
Károly Bezdek, Zsolt Lángi
The structure of -diametral point configurations in Minkowski -space is shown to be closely related to the properties of -antipodal point configurations in .…
From spherical to Euclidean illumination
Károly Bezdek, Zsolt Lángi
In this note we introduce the problem of illumination of convex bodies in spherical spaces and solve it for a large subfamily of convex bodies. We derive from it a combinatorial ve…
Volume of the Minkowski sums of star-shaped sets
Matthieu Fradelizi, Zsolt Lángi, Artem Zvavitch
For a compact set and an integer , let us denote by the Minkowski…
Centering Koebe polyhedra via Möbius transformations
Zsolt Lángi
A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin, and tha…
Tracking critical points on evolving curves and surfaces
Gábor Domokos, Zsolt Lángi, András A. Sipos
In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution of the number of static balance points of the abrading parti…
The isoperimetric quotient of a convex body decreases monotonically under the Eikonal abrasion model
Gábor Domokos, Zsolt Lángi
We show that under the Eikonal abrasion model, prescribing uniform normal speed in the direction of the inward surface normal, the isoperimetric quotient of a convex shape is decre…
On the average number of normals through points of a convex body
Gábor Domokos, Zsolt Lángi
In 1944, Santaló asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The a…
On multiple Borsuk numbers in normed spaces
Zsolt Lángi, Márton Naszódi
Hujter and Lángi introduced the -fold Borsuk number of a set in Euclidean -space of diameter as the smallest cardinality of a family of subsets of $S…