SavedAdd your journal

Journals / 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
Pages
—
Publication Date
2022-04-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

🔖

Cite This Article

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

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  1. Aguglia, A., Cossidente, A., Korchmáros, G.: On quasi–Hermitian varieties. J. Comb. Des. 20, 433–447 (2012).
  2. Calderbank, R., Kantor, W. M.: The geometry of two-weight codes. Bull. London Math. Soc. 18, 97-122 (1986).
  3. De Clerck, F., Hamilton, N., O’ Keefe, C. M., Penttila, T.: Quasi-quadrics and related structures. Aust. J. Combin. 22, 151–166 (2000).
  4. DeWinter, S. Schillewaert, J.: A note on quasi–Hermitian varieties and singular quasi–quadrics. Bull. Belg. Math. Soc. Simon Stevin 17, 911—918 (2010).
  5. Durante, N, Napolitano, V., Olanda, D.: Sets of type (q + 1; n) in PG(3; q). J. Geom. 107, 9–18 (2016). DOI: 10.1007/s00022–015–0271–5
  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
  9. Segre, B.: Ovals in a finite projective plane. Canad. J. Math. 7, 414-–416 (1955).
  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