An improved bound for extending partial projective planes

✍ Scribed by Stephen Dow

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 895 KB
• Volume: 45
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(83)90036-5

✦ Synopsis

A partial projective plane S of order n is a collection of subse:(s (called lines) of an (n' + n + l)-set (of points) such that every line has size n + 1 and any two lines meet in a unique point. We denote the number of lines by b. In this paper it is shown that if b > n* -2(n + 3)f + 6, then 2 can be embedded in a projective plane of order n. Also it is shown that if b > n* -n + 1, then there is at most one such embedding. These results improve previous results of the same form by lowering the required size of b.