Construction and Classification of Complete $(k,3)$-arcs from a Ceva 6-Figure in $PG(2,4)$

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Hagia Sophia Journal of Geometry
Cilt: 7 Sayı: 2
Construction and Classification of Complete $(k,3)$-arcs from a Ceva 6-Figure in $PG(2,4)$

Construction and Classification of Complete $(k,3)$-arcs from a Ceva 6-Figure in $PG(2,4)$

Authors : Elif Altıntaş Kahriman, Ayşe Bayar

Pages : 46-51

View : 47 | Download : 101

Publication Date : 2025-12-29

Article Type : Research Paper

Abstract :This study investigates complete $(k,3)$-arcs generated from a given Ceva 6-figure in the projective plane $PG(2,4)$. The analysis reveals a unique complete $(7,3)$-arc obtained by adding the center point of the Ceva 6-figure, forming a Fano subplane, and eight distinct complete $(9,3)$-arcs constructed by adjoining three points on distinct 2-secant lines. No complete $(8,3)$-arc constructed from the given Ceva 6-figure exists. These results emphasize the combinatorial significance of Ceva-based configurations in finite projective planes and contribute to the systematic understanding of arc structures in finite geometry.
Keywords : projektif düzlem, (k, 3)-ark, tam ark, Ceva 6-figür, sonlu geometri, PG(2, 4)

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