Zsolt Lángi's Homepage

Publications

Publications published in refereed journals
1. K. Bezdek and Z. Lángi, Density bounds for unit ball packings relative to their outer parallel domains, accepted in Pure Appl. Funct. Anal. arxiv:2401.00645, [math.MG]
2. K. Bezdek and Z. Lángi, Remarks on soft ball packings in dimensions 2 and 3, Studia Sci. Math. Hungar. DOI:10.1556/012.2024.04318, arxiv:2310.04574, [math.MG].
3. K. Bezdek and Z. Lángi, On optimal λ-separable packings in the plane, Ars. Math. Contemp., DOI: 10.26493/1855-3974.3130.d46, arXiv:2305.01575 [math.MG].
4. B. Ludmány, Z. Lángi and G. Domokos, Morse-Smale complexes on convex polyhedra, Period. Math. Hungar. 89 (2024), 1-22, DOI: 10.1007/s10998-024-00583-4, arXiv:2106.11626 [cs.CG], [math.CO], [math.MG].
5. K. Bezdek and Z. Lángi, From the separable Tammes problem to extremal distributions of great circles in the unit sphere, Discrete Comput. Geom. 72 (2024), 269–309, DOI: 0.1007/s00454-023-00509-w, arXiv:2201.11234 [math.MG].
6. B. Basit and Z. Lángi, On a Dowker-type problem for convex disks with almost constant curvature, Studia Sci. Math. Hungar. 61 (2024), 59-72, DOI:10.1556/012.2024.04306, arXiv:2308.02378, [math.MG].
7. B. Basit and Z. Lángi, Dowker-type theorems for disk-polygons in normed planes, Discrete Math 347 (2024), 114019, DOI:10.1016/j.disc.2024.114019, arXiv:2307.04026, [math.MG].
8. B. Basit and Z. Lángi, On monohedral tilings of a regular polygon, Aequationes Math. 98 (2024), 535–555, DOI:10.1007/s00010-023-00973-y, arXiv:2109.14264 [math.MG], [math.CO], [math.GT].
9. G. Domokos, Z. Lángi and P. Várkonyi, A characterization of the symmetry groups of mono-monostatic convex bodies, Monatsh. Math. 201 (2023), 703–724, DOI: 10.1007/s00605-023-01847-w.
10. A. Joós and Z. Lángi, Isoperimetric problems for zonotopes, Mathematika 69 (2023), 508-534, DOI:10.1112/mtk.12191, arXiv:2206.03204 [math.MG].
11. B. Basit and Z. Lángi, Discrete isoperimetric problems in spaces of constant curvature, Mathematika 69 (2023), 33-50, DOI:10.1112/mtk.12175, arXiv:2206.04323 [math.MG].
12. M. Kadlicskó and Z. Lángi, On generalized Minkowski arrangements, Ars Math. Contemp. 23 (2023), P1.09, DOI:10.26493/1855-3974.2550.d96, arXiv:2102.03541 [math.MG].
13. G. Domokos and Z. Lángi, Plato's error and a mean field formula for convex mosaics, Axiomathes 32 (2022), 889–905, DOI: 10.1007/s10516-019-09455-w, pdf
14. G. Domokos and Z. Lángi, On some average properties of convex mosaics, Experiment. Math. 31(3) (2022), 783-793. DOI:10.1080/10586458.2019.1691090, arXiv:1905.00721 [math.MG].
15. M. Fradelizi, Z. Lángi and A. Zvavitch, Volume of the Minkowski sums of star-shaped sets, Proc. Amer. Math. Soc. Ser. B 9 (2022), 358-372, DOI:10.1090/bproc/97, arXiv:1910.06146 [math.MG], [math.FA].
16. S.M. Almohammad, Z. Lángi and M. Naszódi, An analogue of a theorem of Steinitz for ball polyhedra in R³, Aequationes Math. 96 (2022), 403-415, DOI:10.1007/s00010-021-00815-9, arXiv:2011.10105 [math.MG], [math.CO].
17. Z. Lángi, A solution to some problems of Conway and Guy on monostable polyhedra, Bull. Lond. Math. Soc. 54(2) (2022), 501-516, DOI:10.1112/blms.12579, arXiv:2008.02090 [math.MG], [math.DG], [math.DS].
18. G. Domokos, Z. Lángi and A.Á. Sipos, Tracking critical points on evolving curves and surfaces, Experiment. Math. 31 (2022), 1-20, DOI:10.1080/10586458.2018.1556136, arXiv:1802.06118 [math.DS], [math-ph], [math.NA].
19. Z. Lángi, An isoperimetric problem for three-dimensional parallelohedra, Pacific J. Math. 316 (2022), 169–181, DOI:10.2140/pjm.2022.316.169, arXiv:2102.11621 [math.MG].
20. Á. G.Horváth and Z. Lángi, On the convex hull and homothetic convex hull functions of a convex body, Geom. Dedicata 216 (2022), article number: 10, DOI:10.1007/s10711-022-00673-y, arXiv:2012.08955 [math.MG].
21. C.L. Ködmön and Z. Lángi, Extremal convex polygons inscribed in a given convex polygon, Comput. Geom. 102 (2022), 101844, DOI:10.1016/j.comgeo.2021.101844, arXiv:2101.03061 [math.MG].
22. K. Bezdek and Z. Lángi, On k-diametral point configurations in Minkowski spaces, Discrete Math. 345 (2022), 112700, DOI:10.1016/j.disc.2021.112700, arXiv:2005.04542 [math.MG].
23. D. Frettlöh, A. Glazyrin and Z. Lángi, Hexagon tilings of the plane that are not edge-to-edge, Acta Math. Hungar., 164 (2021), 341-349, DOI:10.1007/s10474-021-01155-5, arXiv:1911.12752 [math.MG], [math.CO].
24. Z. Lángi, Centering Koebe polyhedra via Möbius transformations, Groups Geom. Dyn. 15 (2021), 197-221, DOI:10.4171/GGD/596, arXiv:1804.07572 [math.MG], [math-DS], [math.GT].
25. G. Domokos, F. Kovács, Z. Lángi, K. Regős and P.T. Varga, Balancing polyhedra, Ars Math. Contemp. 19 (2020), 95-124, DOI:10.26493/1855-3974.2120.085, arXiv:1810.05382 [math.MG].
26. Á. Kurusa, Z. Lángi and V. Vígh, Tiling a circular disc with congruent pieces, Mediterr. J. Math. 17 (2020), article number 156, DOI:10.1007/s00009-020-01595-3, arXiv:1910.03836 [math.GT], [math.MG].
27. K. Bezdek and Z. Lángi, From spherical to Euclidean illumination, Monatsh. Math. 192 (2020), 483-492, DOI: 10.1007/s10516-019-01355-w, arXiv:1909.11884 [math.MG].
28. K. Bezdek and Z. Lángi, Bounds for totally separable translative packings in the plane, Discrete Comput. Geom. 63 (2020), 49-72. DOI:10.1007/s00454-018-0029-6, arXiv:1710.06886 [math.MG].
29. K. Bezdek and Z. Lángi, Minimizing the mean projections of finite ρ-separable packings, Monatsh. Math. 188 (2019), 611-620, DOI:10.1007/s00605-018-1166-y, arXiv:1712.05459 [math.MG].
30. M. Ausserhofer, S. Dann, Z. Lángi and Géza Tóth, An algorithm to find maximum area polygons circumscribed about a convex polygon, Discrete Appl. Math. 255 (2019), 98-108. , DOI:j.dam.2018.08.017, arXiv:1706.08152 (Corrigendum).
31. G. Domokos and Z. Lángi, The isoperimetric quotient of a convex body decreases monotonically under the Eikonal abrasion model, Mathematika 65 (2019), 119-129, arXiv:1801.06796 [math.AP], [math.MG].
32. Z. Lángi, A characterization of affinely regular polygons, Aequationes Math. 92 (2018), 1037-1049, DOI:10.1007/s00010-018-0541-z, arXiv:1706:03036 [math.MG], [math.FA], [math.NT]
33. G. Domokos and Z. Lángi, The evolution of geological shape descriptors under distance-driven flows, Math. Geosci. 54(3) (2018), 337-363, DOI:10.1007/s11004-017-9723-9
34. G. Domokos, Z. Lángi and M. Mezei, A shape evolution model under affine transformations, Mediterr. J. Math. 14 (2017), 210, DOI:10.1007/s00009-017-1008-5, arXiv:1604.07630 [math.MG]
35. Z. Lángi and M. Naszódi, On multiple Borsuk numbers in normed spaces, Studia Sci. Math. Hungar. 54(1) (2017), 13-26, DOI:10.1556/012.2017.54.1.1352, arXiv:1311.3193 [math.MG], [math.CO].
36. Á. G.Horváth, Z. Lángi and M. Spirova, Semi-inner products and the concept of semi-polarity, Results Math. 71(1) (2017), 127-144, DOI:10.1007/s00025-015-0510-y, arXiv:1308.0974 [math.MG], [math.FA].
37. G. Domokos, P. Holmes and Z. Lángi, A genealogy of convex solids via local and global bifurcations of gradient vector fields, J. Nonlinear Sci. 26 (2016), 1789-1815. 10.1007/s00332-016-9319-4, arXiv:1508.04796 [math.MG], [math.ph], [math.DS]
38. J. Frittmann and Z. Lángi, Decompositions of a polygon into centrally symmetric pieces, Mediterr. J. Math. 13 (2016), 3629-3649, DOI:10.1007/s00009-016-0706-8, arXiv:1504.05418 [math.MG], [math.CO].
39. K. Bezdek and Z. Lángi, On non-separable families of positive homothetic convex bodies, Discrete Comput. Geom. 56 (2016), 802-813, DOI:10.1007/s00454-016-9815-1, arXiv:1602.01020 [math.MG].
40. Á. G.Horváth and Z. Lángi, Maximum volume polytopes inscribed in the unit sphere, Monatsh. Math. 181 (2016), 341-354, DOI:10.1007/s00605-016-0949-2, arXiv:1402.6496 [math.MG], [math.CO]
41. Z. Lángi, M. Naszódi, J. Pach, G. Tardos and G. Tóth, Separation with restricted families of sets, J. Combin. Theory Ser. A 144 (2016), 292-305, DOI:10.1016/j.jcta.2016.06.002, arXiv:1508.05504 [math.CO], [math.MG]
42. Z. Lángi, On a normed version of a Rogers-Shephard type problem, Israel J. Math. 202 (2016), 203-217, DOI:10.1007/s11856-016-1284-y, arXiv:1308.2500 [math.MG].
43. G. Domokos, Z. Lángi and T. Szabó, A topological classification of convex bodies, Geom. Dedicata 182 (2016), 95-116, DOI:10.1007/s10711-015-0130-4, arXiv:1204.5494.
44. G. Domokos and Z. Lángi, On the average number of normals through points of a convex body, Studia Sci. Math. Hungar. 52 (2015), 457-476, arXiv:1406.0813 [math.MG].
45. K. Bezdek and Z. Lángi, Density bounds for outer parallel domains of unit ball packings, Proc. Steklov Inst. Math. 288 (2015), 209-225, arXiv:1409.4508 [math.MG].
46. M. Hujter and Z. Lángi, On the multiple Borsuk numbers of sets, Israel J. Math. 199 (2014), 219-239, arXiv:1206.0892v2 [math.MG], [math.CO], June 5, 2012.
47. Á. G.Horváth and Z. Lángi, On the volume of the convex hull of two convex bodies, Monatsh. Math., 174 (2014), 219-229, arXiv:1302.6164v1 [math.MG].
48. G. Domokos and Z. Lángi, The robustness of equilibria on convex solids, Mathematika 60 (2014), 237-256, arXiv:1301.4031v1 [math.MG], [math-ph], [math.DS].
49. Z. Lángi, On the perimeters of simple polygons contained in a plane convex body, Beiträge Algebra Geom. 54 (2013), 643-649, arXiv:1003.2944v1 [math.MG].
50. Z. Lángi, M. Naszódi and I. Talata, Ball and spindle convexity with respect to a convex body, Aequationes Math. 85 (2013), 41-67, arXiv:1110.4823v1 [math.MG], [math.CO].
51. Z. Lángi, Ellipsoid characterization theorems, Adv. Geom. 13(1) (2013), 145-154, arXiv:1105.3334v2 [math.MG], [math:CA].
52. G. Domokos, Z. Lángi and T. Szabó, On the equilibria of finely discretized curves and surfaces, Monatsh. Math. 168 (2012), 321-345, arXiv:1106.0626v2 [math.DG].
53. Z. Lángi, On the Hadwiger numbers of starlike disks, European J. Comb. 32 (2011), 1203-1211, arXiv:1002.3918v3 [math.MG].
54. Z. Lángi, On the perimeters of simple polygons contained in a disk, Monatsh. Math. 162 (2011), 61-67, arXiv:1002.3922v1 [math.MG].
55. Z. Lángi, On universal covers for four-dimensional sets of a given diameter, Rend. Istit. Mat. Univ. Trieste 42 (2010), 59-64, arXiv:1007.2520v2 [math.MG], [math.GT].
56. Z. Lángi, On diagonalizable operators in Minkowski spaces with the Lipschitz property, Lin. Alg. Appl. 433 (2010), 2161-2167, arXiv:1003.2285v5 [math.FA].
57. K. Dehnhardt, H. Harborth and Z. Lángi, A partial proof of the Erdős-Szekeres Conjecture for hexagons, J. Pure Appl. Math., Adv. Appl. 2(1) (2009), 69-86.
58. Z. Lángi and M. Naszódi, On the Bezdek-Pach Conjecture for Centrally Symmetric Convex Bodies, Canad. Math. Bull. 53(3) (2009), 407-415.
59. Z. Lángi, On the Hadwiger numbers of centrally symmetric starlike disks, Beiträge Algebra Geom. 50(1) (2009), 249-257.
60. Z. Lángi, Covering a plane convex body by its negative homothets, J. Geom. 92(1-2) (2009), 91-99.
61. Z. Lángi and M. Naszódi, Kirchberger-type theorems for separation by convex domains, Period. Math. Hungar. 57(2) (2008), 185-196, SCI.
62. A. Joós and Z. Lángi, On the relative distances of seven points in a plane convex body, J. Geom. 87 (2007), 83-95.
63. K. Bezdek, Z. Lángi, M. Naszódi and P. Papez, Ball-polyhedra, Discrete Comput. Geom. 38 (2007), 201-230, SCI. arXiv:1110.4329v1 [math.MG].
64. B. Csikós, Z. Lángi and M. Naszódi, A generalization of the Discrete Isoperimetric Inequality for piecewise smooth curves of constant geodesic curvature, Period. Math. Hungar. 53(1-2) (2006), 121-131.
65. K. Böröczky and Z. Lángi, On the relative distances of six points in a plane convex body, Stud. Sci. Math. Hungar. 42(3) (2005), 253-264, SCI.
66. Z. Lángi, On seven points in the boundary of a plane convex body in large relative distances, Beiträge Algebra Geom. 45(1) (2004), 275-281.
67. Z. Lángi and M. Lassak, Relative distance and packing a body by homothetical copies, Geombinatorics XIII(1) (2003), 29-40.
68. Z. Lángi, Relative distance and a convex body touched by its homothetical copies, Bull. Pol. Ac.:Math. 51(4) (2003), 439-444.
69. Z. Lángi, On the relative lengths of sides of convex polygons, Stud. Sci. Math. Hungar. 40 (2003), 115-120, SCI.
70. Z. Lángi and M. Lassak, On four points of a convex body in large relative distances, Geombinatorics XII(4) (2003), 184-190.
71. K. Bezdek K. and Z. Lángi, On almost equidistant points on S ^d-1, Period. Math. Hungar. 39(1-3) (1999), 139-144.

Other refereed contributions
1. Z. Lángi, Convexity problems in spaces of constant curvature and in normed spaces, Ph.D. thesis, University of Calgary, Calgary, Canada, 2008.
2. Z. Lángi, Relative distance of points of a convex body, Ph.D. thesis, Eötvös University, Budapest, Hungary, 2003.
3. Á. G.Horváth and Z. Lángi, Kombinatorikus geometria, lecture notes, 146 pages, Polygon jegyzettár sorozat, Polygon, Szeged, Hungary, 2012. Contents
4. K. Bezdek and Z. Lángi, Volumetric Discrete Geometry, Discrete Mathematics and Its Applications, CRC Press, Taylor & Francis Group, 2019, 286 pages.

Manuscripts
1. M. Kadlicskó and Z. Lángi, On the edge densities of convex mosaics, arxiv:2312.08050, [math.MG], December 13, 2023.
2. B. Basit, S. Hoehner, Z. Lángi and J. Ledford, Steiner symmetrization on the sphere, arxiv:2406.10614, [math.MG], June 15, 2024.
3. Z. Lángi and S. Wang, The Honeycomb Conjecture in normed planes and an alpha-convex variant of a theorem of Dowker, arXiv:2406.10622, [math.MG], [math.CO], June 15, 2024.
4. Z. Lángi and P.L. Várkonyi, Centroids and equilibrium points of convex bodies, arXiv:2407.19177, [math.MG], July 27, 2024.
5. K. Bezdek and Z. Lángi, On separability in discrete geometry, arXiv:2407.19177, [math.MG], July 27, 2024.
6. K. Bezdek, Z. Lángi and M. Naszódi, Selected topics from the theory of intersections of balls, arXiv:2411.10302, [math.MG], Nov 15, 2024.

Non-refereed publications
1. G. Domokos, F. Kovács, Z. Lángi, K. Regős and P.T. Varga, Konvex poliéderek egyensúlyi pontjai, Középiskolai Matematikai Lapok 70(5) (2020), 264-273.
2. Z. Lángi, Konvex poliéderek stabil lapjai, Középiskolai Matematikai Lapok 69(5) (2019), 258-264.
3. Z. Lángi, Síkidomok csókszáma, Középiskolai Matematikai Lapok 66(4) (2016), 194-199.
4. T. Szabó, G. Domokos and Z. Lángi, Kavicsok morfológiája, In: Levandovszky, János (szerk.) BME Építészmérnöki Kar 2012: PhD műhelyek tanulmányai Budapest, Magyarország : BME Építészmérnöki Kar (2012) pp. 14-17.
5. Z. Lángi, Összefoglaló az IGES adattárolási szabvány geometriai optimalizálásban való közvetlen felhasználásának lehetőségeiről, Jelentés a TÁMOP-4.2.2-08/1-2008-0028 számú pályázathoz, 2011., 168 oldal.
6. Z. Lángi, Az Erdős-Szekeres hatszög probléma, Konferenciakiadvány, Felsőoktatási matematika-, fizika- és számítástechnika oktatók XXXI. konferenciája (Dunaújváros, Hungary, 2007. augusztus 23-25.), 47-52.
7. A. Joós Antal and Z. Lángi, Egy síkbeli konvex test hét pontjának relatív távolsága, A Dunaújvárosi Főisk. Közl. XXVI (2005), 263-280.
8. Z. Lángi, Majdnem egyenlő távolságra levő pontok problémája különböző geometriákban, A Dunaújvárosi Főisk. Közl. XXIII (2002), 263-266.
9. Z. Lángi, Véges sok síkbeli pontra vonatkozó kérdések, Gépgyártástechnológia XXIX(10) (1999), 283-284.
10. Z. Lángi, Egy euklideszi Ramsey-tétel, A Miskolci Egyetem Dunaújvárosi Főisk. Kar Közl. XIX (1998), 159-162.
11. Z. Lángi, Helly tétele többdimenziós euklideszi terekben, A Miskolci Egyetem Dunaújvárosi Főisk. Kar Közl. XIX (1998), 163-166.