University of Tehran
Journal of Sciences, Islamic Republic of Iran
10161104
4
1
1993
03
01
ON THE STRUCTURE OF FINITE
PSEUDO COMPLEMENTS OF
QUADRILATERALS AND THEIR
EMBEDDABILITY

31160
EN
Journal Article
1970
01
01
A pseudocomplement of a quadrilateral D of order n, n, > 3, is a nontrivial (n+l)
regular linear space with n  3n + 3 points and n + n  3 lines. We prove that if n > 18
and D has at least one line of size n  1, or if n > 25 , then the set of lines of D consists of
three lines of size n 1, 6(n  2) lines of size n  2, and n  5n + 6 lines of size n  3.
Furthermore, if n > 21 and D has at least one line of size n  1, then D is embeddable in a
unique projective plane of order n. These results improve the results of the author
https://jsciences.ut.ac.ir/article_31160_2404132375eb45510dd90365c0b1caf5.pdf