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Details of project

 
Identifier
37752
Type K
Principal investigator Heppes, Aladár
Title in Hungarian Diszkrét geometria
Title in English Discrete Geometry
Panel Mathematics and Computing Science
Department or equivalent Department of Geometry (Eötvös Loránd University)
Participants Bezdek, Károly
Böröczky, Károly
Csikós, Balázs
Daróczy Kiss, Endre
Kertész, Gábor
Lángi, Zsolt
Matolcsi, Máté
Visy, Balázs
Starting date 2002-01-01
Closing date 2005-12-31
Funding (in million HUF) 13.116
FTE (full time equivalent) 0.00
state closed project





 

Final report

 
Results in Hungarian
A kutatások folyamán elért új eredmények zömét publikáltuk, illetve közzétételük folyamatban van. A legfontosabb témakörök az alábbiak: Egyoldali Hadwiger szám [5]. Fejes Tóth szoliditási sejtése [12]. Kör/gömb-elhelyezés - Kétféle kört tartalmazó kitöltések [13]. - Minkowski elhelyezések [3], [21]. - Alternatív hatékonysági mértékek [1, 2, 4]. - Tammes probléma (n=13 [9], illetve n=14,15,16 és 17 [7]). - Voronoi celláinak felszínbecslései [24]. Halmazok átmérője Minkowski terek átlósan maximális halmazai [19], Cilindrikus Borsuk-feldarabolások [34]. Jellemzés felület-vágással [23] Petty szám becslés véges normált terekben [6]. Antipodális poliéderek és él-antipodális poliéderek [11, 26] Relatív hossz problémák [16, 17, 18, 22, 28, 36]. Fedési problémák A „nem-keresztezési feltétel” szükségessége [14], illetve az elliptikus sík fedése [15]. Izoperimetrikus problémák mozaikokon [35], geodetikus görbülettű oldalakkal határolt poligonok állandó görbületű síkon [30]. Helly típusú transzverzális problémák [27, 32, 33]. Kneser-Poulsen problémakör [20, 29]. Egyéb publikált eredmények [8], [10], [25], [31].
Results in English
Most of the new results have been published or being published. The most importan topics are as follows: One-sided Hadwiger number [5]. Fejes Tóth’s solidity conjecture [12]. Packing of discs/balls - Two-size packings [13]. - Minkowskian packings [3], [21]. - Alternative efficiency measures [1, 2, 4]. - Tammes’ problem (for n=13 [9], for n=14,15,16 és 17 [7]). - Surface area of Voronoi cells [24]. Diameter of sets Diametrally maximal sets in Minkowskian spaces [19], Cylindrical Borsuk-decomposition [34]. Characterization of sets of constant width by coundary cuts [23] Petty number Estimates in normed spaces [6]. Antipodális poliéderek és él-antipodális poliéderek [11, 26] Relatíve length problems [16, 17, 18, 22, 28, 36]. Covering problems On the possibility of dropping the „non-crossing” assumption [14], the thinnest covering of the elliptic plane by 4 circles [15]. Izoperimetric problems for tilings [35], for polygons bonded by sides of given geodethic curcvature (on planes of constant curvature.) [30]. Helly type transversal problems [27, 32, 33]. Kneser-Poulsen problems [20, 29]. Other published results [8], [10], [25], [31].
Full text http://real.mtak.hu/337/
Decision
Yes





 

List of publications

 
Böröczky K ; Szabó L: Arrangements of 13 points on a sphere, In: Bezdek A (ed.) Discrete Geometry, New York-Basel: Marcel Dekker, 2003. pp. 111-184, 2003
Böröczky K; Szabó L: Minkowski arrangements of circles in the plane, Suppl.Rend.Circ.Mat.Palermo, Ser II/70: 87-92, 2002
Böröczky K ; Lángi Z: On the relative distances of six points in a plane convex body, Stud. Sci. Math. Hungar. 42(3) 253-264, 2005
Bezdek K; Daróczy-Kiss E: Finding the best face on a Voronoi polyhedron - the strong dodecahedral conjecture revisited, Monatshefte fur Math. (elfogadva), 2005
Bezdek K; Naszódi M,: Rigidity of ball-polyhedra in Euclidean 3-space,, European Journal of Combinatorics (elfogadva), 2005
Böröczky K: The Newton-Gregory problem revisited, In: Bezdek A (ed.) Discrete Geometry, New York-Basel: Marcel Dekker, 2003. pp. 103-110, 2003
Böröczky K; Csikós B: Small convex polytops with long edges and many vertices, Discr. Comput. Geom. 30: 195-204, 2003
Bezdek K; Brass P: On k(plus)-neighbour packings and one-sided Hadwiger configurations, Beitrage zur Alg. und Geom. 44/2, 493-498, 2003
Bezdek K; Naszódi M; VisyB: On the m-th Petty numbers of normed spaces, In: Bezdek A (ed.) Discrete Geometry, New York-Basel: Marcel Dekker, 2003. pp. 291-304, 2003
Böröczky ; Szabó L: Arrangements of 14, 15, 16 and 17 points on a sphere, Studia Sci.Math.Hungar. 4Studia Sci.Math.Hungar. 40: 407-7210: 407-721, 2003
Böröczky ; Szabó L: Minkowski arrangements of balls in n-space, Monatshefte d. Math. 141: 11-19, 2004
Csikós B: Edge-antipodal convex polytopes - a proof of Talata's conjecture, In: Bezdek A (ed.) Discrete Geometry, New York-Basel: Marcel Dekker, 2003. pp. 201-205, 2003
Daroczy-Kiss E: A new bound for the minimal diameter of nine coplanar congruent disks, Annales Univ. Sci. Budapest, Sect. Computat.;(elfogadva), 2005
Florian A ; Heppes A: On the non-solidity of some packings and coverings with circles, In: Bezdek A (ed.) Discrete Geometry, New York-Basel: Marcel Dekker, 2003. pp. 279-290, 2003
Heppes A: Some densest two-size disc packings in the plane, Discr. Comput. Geom. 30: 241-262., 2003
Heppes A: Packing of rounded domains on a sphere of constant curvature, Acta Math. Acad.Sci.Hungar.91/3: 245-252, 2001
Heppes A: On the density of 2-saturated lattice packings of discs, Monatsh. Math. 13: 51-66, 2001
Heppes A: Covering the plane with fat ellipses without non-crossing assumption, Discr. Comput. Geom. 29: 477-481, 2003
Heppes A: Expandability radius versus density of a lattice packing, Periodica Math. Hungar. 45/1-2: 65-71, 2002
Heppes A: Az elliptikus sík legritkább fedése négy egybevágó körrel, Mat. Lapok 8-9. (1998-99/1-2) 4-6, 2003
Heppes A: The width of the transversal strips of T(3) families in the plane, Discr. Comput. Geom. 34, 455-461, 2005
Heppes A: New upper bound on the transversal width of T(3)-families of discs, Discr. Comput. Geom. 34, 463-474, 2005
Heppes A; Kuperberg W: Cylindrical partitions of convex bodies, in Combinatorial and Discr. Geom. (Eds. Goodman, Pach, Welzl, MSRI 52, 399-407, 2005
Heppes A; Morgan F: Planar clusters and perimeter bounds, Philosophical Magazine 83/12, 1333-1345, 2005
Lángi Z: On the relative length of sides of convex polygons, Studia Math. Sci. Hungar. 40, 115-120, 2003
Lángi Z: On seven points in the boundary of a plane convex body in large relative distances, Beitr. Alg. Geom., 45(1): 275-281, 2004
Lángi Z: Relative distance and a convex body touched by its homothetical copies, Bull. Pol. Ac.:Math., 51(4): 439-444, 2003
Lángi Z; Lassak M: On four points of a convex body in large relative distances, Geombinatorics XII(4): 184-190, 2003
Lángi Z; Lassak M: Relative distance and packing a body by homothetical copies, Geombinatorics (elfogadva), 2005
Naszódi M; Visy B: Sets with a unique extension to a set of constant width, Discr. Comput. Geom.: 373-380, 2003
Bezdek; R. Connelly; B. Csikós.: On the perimeter of the intersection of congruent disks., Beiträge zur Algebra und Geometrie, (accepted), 2004
Bezdek, K.; T. Bisztriczky; B. Csikós; A. Heppes: On the transversal Helly numbers of disjoint and overlapping discs, Archiv d. Math. (accepted), 2005
Bezdek, K.; M. Naszódi; D. Oliveros-Braniff,: Antipodality in hyperbolic space., Journal of Geometry (accepted), 2005
Csikós, B.: A Schläfli-type formula for polytopes with curved faces and its application to the Kneser-Poulsen conjecture., Monatsh. für Math., 2005. (accepted)., 2005
Csikós, B.; Zs. Lángi; M. Naszódi.: A generalization of the discrete isoperimetric inequality for piecewise smooth curves of constant geodesic curvature., Periodica Math. Hung. (accepted)., 2005
Averkov, G.,A. Heppes,: Constant Minkowkian width in terms of boundary cuts constant geodesic curvature., Rev. Roumaine Math. Pures 50 (2005), 5-6, 423-429., 2005




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