The existence of partitioned balanced tournament designs

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-05-16 DOI:10.1002/jcd.21846

Makoto Araya, Naoya Tokihisa

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引用次数: 0

Abstract

E. R. Lamken proved that there exists a partitioned balanced tournament design of side $n$ , PBTD( $n$ ), for $n$ a positive integer, $n \geq 5$ , except possibly for $n \in {9, 11, 15}$ . In this article, we establish the existence of PBTD( $n$ ) for $n \in {9, 11, 15}$ . As a consequence, the existence of PBTD( $n$ ) has now been completely determined.

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分区平衡锦标赛设计的存在性

E.R.Lamken证明了存在一个边n$n$、PBTD（n$n$$）、边n$n的分区平衡锦标赛设计，对于n$n$一个正整数，n≥5$n\ge 5$，可能除了n∈{9，11，15}$n\in\｛9，11，15\｝$。在本文中，我们建立了n∈n的PBTD（n$n$）的存在性｛9，11，15｝$n\in\｛9、11、15｝$。因此，PBTD（n$n$）的存在现在已经完全确定。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.