How many lines must miss  d  points in a linear space | Zendy

Metsch Klaus | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

How many lines must miss d points in a linear space

Author(s) -

Metsch Klaus

Publication year - 2006

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20116

Subject(s) - mathematics , combinatorics , linear space , space (punctuation) , projective plane , projective space , plane (geometry) , algebraic number , degenerate energy levels , discrete mathematics , point (geometry) , geometry , pure mathematics , projective test , mathematical analysis , philosophy , linguistics , physics , quantum mechanics , correlation

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

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research