Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T ( q 3 , q ) in PG ( 7 , q 3 )

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2026-05-28 Epub Date: 2026-04-06 DOI:10.1002/jcd.70014

Sebastian Petit, Geertrui Van de Voorde

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引用次数: 0

Abstract

In this paper, we study and characterise the natural embedding of the twisted triality hexagon $T (q^{3}, q)$ in $PG (7, q^{3})$ . We begin by describing the possible intersections of subspaces of $PG (7, q^{3})$ with $T (q^{3}, q)$ . Then, we provide conditions on a set of lines $ℒ$ , which ensure that $ℒ$ forms the line set of a naturally embedded twisted triality hexagon. This work follows up on similar results for the split Cayley hexagon by J. A. Thas and H. Van Maldeghem (2008) and F. Ihringer (2014).

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扭曲三态六边形T （q3,）自然嵌入的交数q) in PG （7, q 3）

在本文中，研究并刻画了扭曲三态六边形T （q3）的自然嵌入,(7)， q 3)。我们首先描述PG (7，q3)与T(q3；问：在此基础上，给出了一组线的条件，证明了线是自然嵌入的扭曲三角六边形的线集。这项工作是继j.a. Thas和H. Van Maldeghem（2008）以及F. Ihringer（2014）对分裂的Cayley六边形的类似结果之后进行的。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.