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...
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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 |
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http://dx.doi.org/10.1478/AAPP.96S2A7
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doaj-117fc2e199b643489a40d335e56c63c9 |
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doaj-117fc2e199b643489a40d335e56c63c92020-11-24T20:52:52ZengAccademia Peloritana dei PericolantiAtti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali0365-03591825-12422018-11-0196S2A710.1478/AAPP.96S2A7AAPP.96S2A7On the parameters of two-intersection sets in PG(3, q)Stefano InnamoratiFulvio ZuanniIn 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. http://dx.doi.org/10.1478/AAPP.96S2A7 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Stefano Innamorati Fulvio Zuanni |
| spellingShingle |
Stefano Innamorati Fulvio Zuanni On the parameters of two-intersection sets in PG(3, q) Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| author_facet |
Stefano Innamorati Fulvio Zuanni |
| author_sort |
Stefano Innamorati |
| title |
On the parameters of two-intersection sets in PG(3, q) |
| title_short |
On the parameters of two-intersection sets in PG(3, q) |
| title_full |
On the parameters of two-intersection sets in PG(3, q) |
| title_fullStr |
On the parameters of two-intersection sets in PG(3, q) |
| title_full_unstemmed |
On the parameters of two-intersection sets in PG(3, q) |
| title_sort |
on the parameters of two-intersection sets in pg(3, q) |
| publisher |
Accademia Peloritana dei Pericolanti |
| series |
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| issn |
0365-0359 1825-1242 |
| publishDate |
2018-11-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1478/AAPP.96S2A7
|
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AT stefanoinnamorati ontheparametersoftwointersectionsetsinpg3q AT fulviozuanni ontheparametersoftwointersectionsetsinpg3q |
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