| Title:
|
Improvement of inequalities for the $(r,q)$-structures and some geometrical connections (English) |
| Author:
|
Bálint, Vojtech |
| Author:
|
Lauron, Philippe |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
283-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
structure |
| Keyword:
|
line |
| Keyword:
|
circle |
| Keyword:
|
horocycle |
| MSC:
|
05B30 |
| MSC:
|
51E30 |
| MSC:
|
52C10 |
| idZBL:
|
Zbl 0846.05012 |
| idMR:
|
MR1390587 |
| . |
| Date available:
|
2008-06-06T21:29:26Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107549 |
| . |
| Reference:
|
[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 0675948 |
| Reference:
|
[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 1261471 |
| Reference:
|
[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 1643894 |
| Reference:
|
[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 0729781 |
| Reference:
|
[5] Borwein, P., Moser, W. O. J.: A survey of Sylvester’s problem and its generalizations.Aequa. Math. 40 (1990), 111-135. MR 1069788 |
| Reference:
|
[6] de Bruijn, N. G., Erdős, P.: On a combinatorical problem.Nederl. Acad. Wetensch. 51 (1948), 1277-1279. MR 0028289 |
| Reference:
|
[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 1194036 |
| Reference:
|
[8] Elekes, G.: $n$ points in the plane can determine $n^{3\over 2}$ unit circles.Combinatorica 4 (1984), 131. Zbl 0561.52009, MR 0771719 |
| Reference:
|
[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. Zbl 0163.14701, MR 0213939 |
| Reference:
|
[10] Erdős, P.: Néhány geometriai problémáról.Mat. Lapok 8 (1957), 86-92. MR 0098072 |
| Reference:
|
[11] Erdős, P.: On some metric and combinatorical geometric problems.Discrete Math. 60 (1986), 147-153. MR 0852104 |
| Reference:
|
[12] Hansen, S.: Contributions to the Sylvester-Gallai-Theory.Doctoral dissertation, University of Copenhagen, 1981. |
| Reference:
|
[13] Harborth, H., Mengersen, I.: Point sets with many unit circles.Discrete Math. 60 (1985), 193-197. MR 0852106 |
| Reference:
|
[14] Harborth, H.: Einheitskreise in ebenen Punktmengen.3.Kolloquium über Diskrete Geometrie, Institut für Mathematik der Universität Salzburg (1985), 163-168. Zbl 0572.52020 |
| Reference:
|
[15] Jucovič, E.: Problem $24$.Combinatorical Structures and their Applications, New York-London-Paris, Gordon and Breach, 1970. |
| Reference:
|
[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 0097014 |
| Reference:
|
[17] Klee, V., Wagon, S.: Old and New Unsolved Problems in Plane Geometry and Number Theory.Mathematical Assoc. Amer., Washington, DC, 1991. MR 1133201 |
| Reference:
|
[18] Sylvester, J. J.: Mathematical Question $11851$.Educational Times 59 (1893), 98. |
| . |
