Characterising ovoidal cones by their hyperplane intersection numbers

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2024-10-09 DOI:10.1002/jcd.21959

Bart De Bruyn, Geertrui Van de Voorde

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Abstract

In this paper, we characterise point sets having the same intersection numbers with respect to hyperplanes as an ovoidal cone. In particular, we show that a set of points of $PG (4, q)$ which blocks all planes and intersects solids in $q + 1$ , $q^{2} + 1$ or $q^{2} + q + 1$ points is a plane or an ovoidal cone, and determine all examples that arise when the blocking condition is omitted.

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通过超平面相交数确定卵圆锥的特征

在本文中，我们描述了相对于超平面具有与卵圆锥相同交点数的点集的特征。特别是，我们证明了 PG ( 4 , q ) $\text{PG}(4,q)$ 的点集阻塞所有平面并与实体相交于 q + 1 $q+1$ 、q 2 + 1 ${q}^{2}+1$ 或 q 2 + q + 1 ${q}^{2}+q+1$ 点是平面或卵圆锥，并确定了省略阻塞条件时出现的所有例子。

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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.