Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2022, Cilt: 15 Sayı: 1, 79 - 82, 30.04.2022
https://doi.org/10.36890/iejg.1049258

Öz

In this paper (q2+q+1)(q2+q+1)-sets of points in PG(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 qq odd a characterization of quadratic cones is obtained.

Kaynakça

  • [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
Yıl 2022, Cilt: 15 Sayı: 1, 79 - 82, 30.04.2022
https://doi.org/10.36890/iejg.1049258

Öz

Kaynakça

  • [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
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Vito Napolitano 0000-0002-2504-6967

Erken Görünüm Tarihi 30 Nisan 2022
Yayımlanma Tarihi 30 Nisan 2022
Kabul Tarihi 8 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 15 Sayı: 1

Kaynak Göster

APA 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, 15(1), 79-82. https://doi.org/10.36890/iejg.1049258
AMA Napolitano V. On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$. Int. Electron. J. Geom. Nisan 2022;15(1):79-82. doi:10.36890/iejg.1049258
Chicago Napolitano, Vito. “On $(q^2+q+1)$-Sets of Plane-Type $(m, N, r)_2$ in $\mathrm{PG}(3, q)$”. International Electronic Journal of Geometry 15, sy. 1 (Nisan 2022): 79-82. https://doi.org/10.36890/iejg.1049258.
EndNote Napolitano V (01 Nisan 2022) On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$. International Electronic Journal of Geometry 15 1 79–82.
IEEE V. Napolitano, “On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$”, Int. Electron. J. Geom., c. 15, sy. 1, ss. 79–82, 2022, doi: 10.36890/iejg.1049258.
ISNAD Napolitano, Vito. “On $(q^2+q+1)$-Sets of Plane-Type $(m, N, r)_2$ in $\mathrm{PG}(3, q)$”. International Electronic Journal of Geometry 15/1 (Nisan 2022), 79-82. https://doi.org/10.36890/iejg.1049258.
JAMA Napolitano V. On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$. Int. Electron. J. Geom. 2022;15:79–82.
MLA Napolitano, Vito. “On $(q^2+q+1)$-Sets of Plane-Type $(m, N, r)_2$ in $\mathrm{PG}(3, q)$”. International Electronic Journal of Geometry, c. 15, sy. 1, 2022, ss. 79-82, doi:10.36890/iejg.1049258.
Vancouver Napolitano V. On $(q^2+q+1)$-Sets of Plane-Type $(m, n, r)_2$ in $\mathrm{PG}(3, q)$. Int. Electron. J. Geom. 2022;15(1):79-82.