Improvement of inequalities for the \((r,q)\)-structures and some geometrical connections. (English) Zbl 0846.05012

Bálint, Vojtech; Lauron, Philippe

Arch. Math., Brno 31, No. 4, 283-289 (1995).

Summary: The main results are the inequalities \(m\geq n\) and \(m\geq \sqrt{{rq(q- 1)\over n}(\begin{smallmatrix} n\\ r\end{smallmatrix})}\) for the minimal number of \((r, q)\)-structure classes, which improve the ones from our paper [Studies of University of Transport and Communication in Žilina, Math.-Phys. Ser. 10, 3-10 (1995)], and also some geometrical connections.

MSC:

05B30	Other designs, configurations
51E30	Other finite incidence structures (geometric aspects)

Keywords:

structure; circle; horocycle; line