Bálint, Vojtech Extension of certain combinatorial estimates with geometrical background. (English) Zbl 0959.05012 Period. Math. Hung. 39, No. 1-3, 135-138 (1999). Summary: Combinatorial inequalities and some of their geometrical consequences are generalized. MSC: 05A20 Combinatorial inequalities 52C99 Discrete geometry Keywords:combinatorial inequalities; geometric structures PDF BibTeX XML Cite \textit{V. Bálint}, Period. Math. Hung. 39, No. 1--3, 135--138 (1999; Zbl 0959.05012) Full Text: DOI References: [1] BÁlint, V., On a certain class of incidence structures, Práce a štúdie Vysokej školy dopravnej v Žiline, 2, 97-106 (1979) · Zbl 0449.51001 [2] BÁlint, V., On a connection between unit circles and horocycles determined by n points, Period. Math. Hungar., 38, 15-17 (1999) · Zbl 0936.52006 [3] V. BÁlint, One combinatorial theorem and two of its geometrical corollaries, in: Research Communications of the conference held in the memory of Paul Erdős, Budapest, Hungary, July 4-11, 1999, 27-29. · Zbl 1109.52303 [4] BÁlint, V.; BÁlintovÁ, A., On the number of circles determined by n points in Euclidean plane, Acta Math. Hungar., 63, 283-289 (1994) · Zbl 0796.51008 [5] V. BÁlint, M. BranickÁ, P. GreŠÁk, P. NovotnÝ AND M. Stacho, Realizability of combinatorial (r,q)-structures in the geometrical models, Studies of University of Transport and Communications in Žilina, 1999, in print. · Zbl 1054.05013 [6] BÁlint, V.; Lauron, P., Improvement of inequalities for the (r,q)-structures and some geometrical connections, Archivum mathematicum, 31, 4, 283-289 (1995) · Zbl 0846.05012 [7] Beck, J., On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry, Combinatorica, 3, 281-297 (1983) · Zbl 0533.52004 [8] A. Bezdek, F. Fodor AND I. Talata, On Sylvester type theorems for unit circles, Disc. Math. Special volume in honour of Helge Tverberg (1998), 1-6. [9] de Bruijn, N. G.; ErdŐs, P., On a combinatorial problem, Nederl. Acad. Wetensch., 51, 1277-1279 (1948) · Zbl 0032.24405 [10] H. S. M. Coxeter, Introduction to geometry, John Wiley and Sons, 1961. · Zbl 0095.34502 [11] Csima, J.; Sawyer, E. T., A short proof that there exist 6n/13 ordinary points, Discrete and Comput. Geometry, 9, 187-202 (1993) · Zbl 0771.52003 [12] Elliott, P. D. T. A., On the number of circles determined by n points, Acta. Math. Hungar., 18, 181-188 (1967) · Zbl 0163.14701 [13] ErdŐs, P., Néhány geometriai problémáról, Mat. Lapok, 8, 86-92 (1957) · Zbl 0102.37004 [14] ErdŐs, P., On the combinatorial problems which I would most like to see solved, Combinatorica, 1, 25-42 (1981) · Zbl 0486.05001 [15] ErdŐs, P., Combinatorial problems in geometry, Math. Chronicle, 12, 35-54 (1983) · Zbl 0537.51017 [16] GrÜnbaum, B., Arrangements and Spreads (1972), Providence, Rhode Island: Amer. Math. Soc., Providence, Rhode Island · Zbl 0249.50011 [17] S. Hansen, Contributions to the Sylvester-Gallai Theory, Doctoral dissertation, University of Copenhagen, 1981. [18] JucoviČ, E., Beitrag zur kombinatorischen Inzidenzgeometrie, Acta Math. Acad. Sci. Hungar., 18, 255-259 (1967) · Zbl 0155.30002 [19] JucoviČ, E., Problem 24. Combinatorial Structures and their Applications (1970), New York-London-Paris: Gordon and Breach, New York-London-Paris [20] Kelly, L. M.; Moser, W. O. J., On the number of ordinary lines determined by n points, Canad. J. of Math., 10, 210-219 (1958) · Zbl 0081.15103 [21] KoutskÝ, K.; PolÁk, V., Poznámka o postradatelných bodech v úplných sestavách bodů a přímek v rovině, Časopis pro pěstování matematiky, 85, 60-69 (1960) [22] Klee, V.; Wagon, S., Old and New Unsolved Problems in Plane Geometry and Number Theory (1991), Washington DC: Math. Assoc. Amer., Washington DC · Zbl 0784.51002 [23] W. O. J. Moser AND J. Pach, Research Problems in Discrete Geometry Privately published collection of problems, 1994. [24] Sylvester, J. J., Mathematical Question 11851, Educational Times, 59, 98 (1893) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.