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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 15 Issue: 1

On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$

Vito Napolitano(Università della Campania Luigi Vanvitelli)0000-0002-2504-6967
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Yayın Tarihi
2022-04-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper ( q 2 + q + 1 ) (q2+q+1) -sets of points in P G ( 3 , q ) PG(3,q) of type ( m , n , r ) (m,n,r) with respect to planes are studied, and as a by-product for q q odd a characterization of quadratic cones is obtained.

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Amaç & Hipotez:In this paper ( q 2 + q + 1 ) (q2+q+1) -sets of points in P G ( 3 , q ) PG(3,q) of type ( m , n , r ) (m,n,r) with respect to planes are studied, and as a by-product for q q odd a characterization of quadratic cones is obtained.
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Temel Bulgular & Veri:In this paper ( q 2 + q + 1 ) (q2+q+1) -sets of points in P G ( 3 , q ) PG(3,q) of type ( m , n , r ) (m,n,r) with respect to planes are studied, and as a by-product for q q odd a characterization of quadratic cones is obtained.
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Sonuç & Katkı:In this paper ( q 2 + q + 1 ) (q2+q+1) -sets of points in P G ( 3 , q ) PG(3,q) of type ( m , n , r ) (m,n,r) with respect to planes are studied, and as a by-product for q q odd a characterization of quadratic cones is obtained.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Projective spaces · intersection numbers · oval

Abstract

In this paper ( q 2 + q + 1 ) (q2+q+1) -sets of points in P G ( 3 , q ) PG(3,q) of type ( m , n , r ) (m,n,r) with respect to planes are studied, and as a by-product for q q odd a characterization of quadratic cones is obtained.

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Bu Makaleye Atıf Yap

Napolitano, V. (2022). On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$. International Electronic Journal of Geometry, Volume: 15 Issue: 1. https://doi.org/10.36890/iejg.1049258

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Kaynakça (12)

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  6. Napolitano, V.: A characterization of the Hermitian variety in finite 3-dimensional projective spaces. The Electronic Journal of Combinatorics. 22 (1), 1–22 (2015).
  7. Napolitano, V.: On quasi–Hermitian varieties in PG(3; q2). Discrete Math. 339, 511–514 (2016). DOI 10.1016/j.disc.2015.09.013
  8. Napolitano V.: Cones in PG(3; q). Note Mat. 40 ( 1), 81–86 (2020). DOI:10.1285/i15900932v40n1p81
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  10. Zannetti, M.: A combinatorial characterization of parabolic quadrics, Journal of Discrete Mathematical Sciences and Cryptography 12 (6), 707-715 (2009). DOI: 10.1080/09720529.2009.10698266
  11. Zuanni F.: A characterization of the oval cone in PG(3; q), Journal of Discrete Mathematical Sciences and Cryptography 24 (3), 859–863 (2021). DOI 10.1080/09720529.2021.1895506
  12. Napolitano, V.: On quasi–Hermitian varieties in PG(3; q2). Discrete Math. 339, 511–514 (2016). DOI 10.1016/j.disc.2015.09.013