Institution: | aDipartimento di Matematica, Università degli Studi della Basilicata, Campus Macchia Romana, Contrada Macchia Romana, 85100 Potenza, Italy |
Abstract: | A famous result of de Bruijn and Erdős (Indag. Math. 10 (1948) 421–423) states that a finite linear space has at least as many lines as points, with equality only if it is a projective plane or a near-pencil. This result led to the problem of characterizing finite linear spaces for which the difference between the number b of lines and the number v of points is assigned. In this paper finite linear spaces with b−v m, m being the minimum number of lines on a point, are characterized. |