On the parameters of two-intersection sets in PG(3, q)
In this paper we study the behaviour of the admissible parameters of a two-intersection set in the finite three-dimensional projective space of order q=p^h a prime power. We show that all these parameters are congruent to the same integer modulo a power of p. Furthermore, when the difference of the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Peloritana dei Pericolanti
2018-11-01
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| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: |
http://dx.doi.org/10.1478/AAPP.96S2A7
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| Summary: | In this paper we study the behaviour of the admissible parameters of a two-intersection set in the finite three-dimensional projective space of order q=p^h a prime power. We show that all these parameters are congruent to the same integer modulo a power of p. Furthermore, when the difference of the intersection numbers is greater than the order of the underlying geometry, such integer is either 0 or 1 modulo a power of p. A useful connection between the intersection numbers of lines and planes is provided. We also improve some known bounds for the cardinality of the set. Finally, as a by-product, we prove two recent conjectures due to Durante, Napolitano and Olanda. |
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| ISSN: | 0365-0359 1825-1242 |