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
Language:English
Published: University of Tehran 1993-03-01
Series:Journal of Sciences, Islamic Republic of Iran
Online Access:https://jsciences.ut.ac.ir/article_31160_2404132375eb45510dd90365c0b1caf5.pdf
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collection DOAJ
description 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
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publishDate 1993-03-01
publisher University of Tehran
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series Journal of Sciences, Islamic Republic of Iran
spelling doaj-art-724371bef33e491e9915db1e41e891402025-08-20T03:13:36ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69141993-03-014131160ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITYA 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 authorhttps://jsciences.ut.ac.ir/article_31160_2404132375eb45510dd90365c0b1caf5.pdf
spellingShingle ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
Journal of Sciences, Islamic Republic of Iran
title ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
title_full ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
title_fullStr ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
title_full_unstemmed ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
title_short ON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
title_sort on the structure of finite pseudo complements of quadrilaterals and their embeddability
url https://jsciences.ut.ac.ir/article_31160_2404132375eb45510dd90365c0b1caf5.pdf