关于强 Skolem 启动器的产物

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2024-05-07 DOI:10.1002/jcd.21943

Oleg Ogandzhanyants, Margarita Kondratieva, Nabil Shalaby

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引用次数: 0

摘要

1991 年，沙拉比猜想，任何，其中或，都承认一个强 Skolem 起子。2018 年，作者全面描述并明确构建了强 Skolem 起子的无限 "心形 "族。迄今为止，人们还不知道这些组合设计的其他无限族。本文证明的关于起始器乘积的声明给出了一种生成复合阶强或倾斜斯科莱姆起始器的新方法。这种方法扩展了我们之前的结果，生成了这些起始数的新的无穷族，它们不是心形的。

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On products of strong Skolem starters

In 1991, Shalaby conjectured that any $Z_{n}$ , where $n \equiv 1$ or $3 (\mod 8), n \geq 11$ , admits a strong Skolem starter. In 2018, the authors fully described and explicitly constructed the infinite “cardioidal” family of strong Skolem starters. No other infinite family of these combinatorial designs was known to date. Statements regarding the products of starters, proven in this paper give a new way of generating strong or skew Skolem starters of composite orders. This approach extends our previous result by generating new infinite families of these starters that are not cardioidal.

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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.