关于P - G - L （2, q）的3-设计

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2025-07-28 DOI:10.1002/jcd.22000

Paul Tricot

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Thus, an orbit of its action on the <math>\n <semantics>\n <mrow>\n \n <mrow>\n <mi>k</mi>\n </mrow>\n </mrow>\n </semantics></math>-subsets of the projective line is the block set of a 3-<math>\n <semantics>\n <mrow>\n \n <mrow>\n <mrow>\n <mo>(</mo>\n \n <mrow>\n <mi>q</mi>\n \n <mo>+</mo>\n \n <mn>1</mn>\n \n <mo>,</mo>\n \n <mi>k</mi>\n \n <mo>,</mo>\n \n <mi>λ</mi>\n </mrow>\n \n <mo>)</mo>\n </mrow>\n </mrow>\n </mrow>\n </semantics></math> design. 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引用次数: 0

摘要

组P G L (2，q) 3传递作用于投影线gf (Q)∪{∞}。因此,它作用于投影线的k个子集的轨道是一个3- (q)的块集+ 1, k, λ)设计。我们找到了由< θ r >形式的块的轨道形成的设计参数或者< θ r >∪b{0}；其中θ是gf (q) .

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On 3-Designs From P G L ( 2 , q )

The group $P G L (2, q)$ acts 3-transitively on the projective line $G F (q) \cup {\infty}$ . Thus, an orbit of its action on the $k$ -subsets of the projective line is the block set of a 3- $(q + 1, k, λ)$ design. We find the parameters of the designs formed by the orbit of a block of the form $〈 θ^{r} 〉$ or $〈 θ^{r} 〉 \cup {0}$ , where $θ$ is a primitive element of $G F (q)$ .

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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.