Geodesic
Improvement of inequalities for the $(r,q)$-structures and some geometrical connections
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 283-289
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The main results are the inequalities (1) and (6) for the minimal number of $(r,q)$-structure classes,which improve the ones from [3], and also some geometrical connections, especially the inequality (13).
The main results are the inequalities (1) and (6) for the minimal number of $(r,q)$-structure classes,which improve the ones from [3], and also some geometrical connections, especially the inequality (13).
Classification : 05B30, 51E30, 52C10
Keywords: structure; line; circle; horocycle 
@article{ARM_1995_31_4_a4,
     author = {B\'alint, Vojtech and Lauron, Philippe},
     title = {Improvement of inequalities for the $(r,q)$-structures and some geometrical connections},
     journal = {Archivum mathematicum},
     pages = {283--289},
     year = {1995},
     volume = {31},
     number = {4},
     mrnumber = {1390587},
     zbl = {0846.05012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a4/}
}
TY  - JOUR
AU  - Bálint, Vojtech
AU  - Lauron, Philippe
TI  - Improvement of inequalities for the $(r,q)$-structures and some geometrical connections
JO  - Archivum mathematicum
PY  - 1995
SP  - 283
EP  - 289
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a4/
LA  - en
ID  - ARM_1995_31_4_a4
ER  - 
%0 Journal Article
%A Bálint, Vojtech
%A Lauron, Philippe
%T Improvement of inequalities for the $(r,q)$-structures and some geometrical connections
%J Archivum mathematicum
%D 1995
%P 283-289
%V 31
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a4/
%G en
%F ARM_1995_31_4_a4
Bálint, Vojtech; Lauron, Philippe. Improvement of inequalities for the $(r,q)$-structures and some geometrical connections. Archivum mathematicum, Tome 31 (1995) no. 4, pp. 283-289. http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a4/

[1] Bálint, V.: On a certain class of incidence structures. Práce a štúdie Vysokej Školy Dopravnej v Žiline 2 (1979), 97-106 (In Slovak; summary in English, German and Russian). | MR

[2] Bálint, V., Bálintová, A.: On the number of circles determined by $n$ points in Euclidean plane. Acta Mathematica Hungarica 63 (3-4) (1994), 283-289. | MR

[3] Bálint, V., Lauron, Ph.: Some inequalities for the $(r,q)$-structures. STUDIES OF UNIVERSITY OF TRANSPORT AND COMMUNICATIONS IN ŽILINA, Mathematical - Physical Series, Volume 10 (1995), 3-10. | MR

[4] Beck, J.: On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorical geometry. Combinatorica 3 (3-4) (1983), 281-297. | MR

[5] Borwein, P., Moser, W. O. J.: A survey of Sylvester’s problem and its generalizations. Aequa. Math. 40 (1990), 111-135. | MR

[6] de Bruijn, N. G., Erdős, P.: On a combinatorical problem. Nederl. Acad. Wetensch. 51 (1948), 1277-1279. | MR

[7] Csima, J., Sawyer, E. T.: A short proof that there exist $6n/13$ ordinary points. Discrete and Computational Geometry 9 (1993), no. 2, 187-202. | MR

[8] Elekes, G.: $n$ points in the plane can determine $n^{3\over 2}$ unit circles. Combinatorica 4 (1984), 131. | MR | Zbl

[9] Elliott, P. D. T. A.: On the number of circles determined by $n$ points. Acta Math. Acad. Sci. Hung. 18 (3-4) (1967), 181-188. | MR | Zbl

[10] Erdős, P.: Néhány geometriai problémáról. Mat. Lapok 8 (1957), 86-92. | MR

[11] Erdős, P.: On some metric and combinatorical geometric problems. Discrete Math. 60 (1986), 147-153. | MR

[12] Hansen, S.: Contributions to the Sylvester-Gallai-Theory. Doctoral dissertation, University of Copenhagen, 1981.

[13] Harborth, H., Mengersen, I.: Point sets with many unit circles. Discrete Math. 60 (1985), 193-197. | MR

[14] Harborth, H.: Einheitskreise in ebenen Punktmengen. 3.Kolloquium über Diskrete Geometrie, Institut für Mathematik der Universität Salzburg (1985), 163-168. | Zbl

[15] Jucovič, E.: Problem $24$. Combinatorical Structures and their Applications, New York-London-Paris, Gordon and Breach, 1970.

[16] Kelly, L. M., Moser, W. O. J.: On the number of ordinary lines determined by $n$ points. Canad. J. Math. 10 (1958), 210-219. | MR

[17] Klee, V., Wagon, S.: Old and New Unsolved Problems in Plane Geometry and Number Theory. Mathematical Assoc. Amer., Washington, DC, 1991. | MR

[18] Sylvester, J. J.: Mathematical Question $11851$. Educational Times 59 (1893), 98.