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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2022 / Cilt: 15 Sayı: 2

On The Fano Planes in (7n-1)-dimensional Projective Spaces

(7n-1)-Boyutlu Projektif Uzayda Fano Düzlemleri Üzerine

Ziya Akça(ESKISEHIR OSMANGAZI UNIVERSITY, FACULTY OF SCIENCE AND LETTERS)0000-0001-6379-0546
Abdilkadir Altıntaş(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0002-7012-352X
Pages
442–447
Publication Date
2022-08-31
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AI Summary & Key Takeaways

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

We give examples of Fano planes whose the lines of Fano configuration are planes and the points are points of PG(6,2) and the lines of Fano configuration are 5-spaces and the points are lines of PG(13,2).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we obtain Fano planes whose points are (n-1)-dimensional subspaces and lines are (3n-1)- dimensional subspaces of P in (7n-1)-dimensional projective space P ,using (n;k)-SCID.
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Key Findings & Data:In this study, we obtain Fano planes whose points are (n-1)-dimensional subspaces and lines are (3n-1)- dimensional subspaces of P in (7n-1)-dimensional projective space P ,using (n;k)-SCID.
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Conclusion & Impact:We give examples of Fano planes whose the lines of Fano configuration are planes and the points are points of PG(6,2) and the lines of Fano configuration are 5-spaces and the points are lines of PG(13,2).
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Klein dönüşümü · Gömme · Latin ve Greek Düzlemleri

Abstract

In this study, we obtain Fano planes whose points are (n-1)-dimensional subspaces and lines are (3n-1)- dimensional subspaces of P in (7n-1)-dimensional projective space P ,using (n;k)-SCID. We give examples of Fano planes whose the lines of Fano configuration are planes and the points are points of PG(6,2) and the lines of Fano configuration are 5-spaces and the points are lines of PG(13,2).

Özet

Bu çalışmada, (n:k)-SCID kullanarak (7n-1)-boyutlu P projektif uzayında noktaları P nin (n-1)-boyutlu alt uzayları ve doğruları P nin (3n-1)-boyutlu alt uzayları olan Fano düzlemleri elde ediyoruz. de noktaları noktalar ve doğruları düzlemler olan ve de noktaları doğrular ve doğruları 5-uzaylar olan Fano düzlemlerinin örneklerini veriyoruz.

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Cite This Article

Akça, Z., Altıntaş, A., *, Z. A. (2022). On The Fano Planes in (7n-1)-dimensional Projective Spaces. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 Sayı: 2, 442–447. https://doi.org/10.18185/erzifbed.982509

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