How many lines must miss d points in a linear space

✍ Scribed by Klaus Metsch

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 113 KB
• Volume: 14
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20116

✦ Synopsis

Abstract

It was remarked by P. Erdős, J. C. Fowler, V. T. Sós, and R. M. Wilson, (J Combin Theory Ser A 38, 1985, 131–142), that a non‐degenerate finite linear space on v points has the following property. For every point P the number of lines not passing through P is at least $\lfloor v-\sqrt v\rfloor$ with equality if and only if the linear space is a projective plane. We give a short proof for this result using an algebraic tool. The main purpose of the article however is to generalize this result in the direction that gives a lower bound for the number of lines not passing through a given number d of points. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 441–450, 2006