ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
A pseudo-complement of a quadrilateral D of order n, n, > 3, is a non-trivial (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...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1993-03-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31160_2404132375eb45510dd90365c0b1caf5.pdf |
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| Summary: | A pseudo-complement of a quadrilateral D of order n, n, > 3, is a non-trivial (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 |
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| ISSN: | 1016-1104 2345-6914 |