大集合可分解幂等拉丁平方的谱

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-07-27 DOI:10.1002/jcd.21853

Xiangqian Li, Yanxun Chang

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Hence, there exists an LRILS(v) for any positive integer <math>\n <semantics>\n <mrow>\n <mi>v</mi>\n \n <mo>≥</mo>\n \n <mn>3</mn>\n </mrow>\n <annotation> $v\\ge 3$</annotation>\n </semantics></math>, except <math>\n <semantics>\n <mrow>\n <mi>v</mi>\n \n <mo>=</mo>\n \n <mn>6</mn>\n </mrow>\n <annotation> $v=6$</annotation>\n </semantics></math>.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"30 10","pages":"671-683"},"PeriodicalIF":0.5000,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The spectrum for large sets of resolvable idempotent Latin squares\",\"authors\":\"Xiangqian Li, Yanxun Chang\",\"doi\":\"10.1002/jcd.21853\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An idempotent Latin square of order <math>\\n <semantics>\\n <mrow>\\n <mi>v</mi>\\n </mrow>\\n <annotation> $v$</annotation>\\n </semantics></math> is called resolvable and denoted by RILS(v) if the <math>\\n <semantics>\\n <mrow>\\n <mi>v</mi>\\n <mrow>\\n <mo>(</mo>\\n <mrow>\\n <mi>v</mi>\\n \\n <mo>−</mo>\\n \\n <mn>1</mn>\\n </mrow>\\n \\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation> $v(v-1)$</annotation>\\n </semantics></math> off-diagonal cells can be resolved into <math>\\n <semantics>\\n <mrow>\\n <mi>v</mi>\\n \\n <mo>−</mo>\\n \\n <mn>1</mn>\\n </mrow>\\n <annotation> $v-1$</annotation>\\n </semantics></math> disjoint transversals. 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引用次数: 0

摘要

v$v$阶的幂等拉丁方称为可分解的，并用RILS（v）表示，如果v（v−1）$v（v-1）$off对角线单元格可以分解为v−1$v-1$不相交的横截面。一个v$v$阶的可分解幂等拉丁平方的大集合，是v−2$v-2$RILS（v）s仅在主对角线上成对一致的集合。在本文中，对于v∈，构造了一个LRILS（v）{14，20，22，28，34、35、38、40，42、46、50、55，62｝$v\in\｛14,20,22,28,34,35,38,40,42,46,50,55,62\｝$。因此，对于任何正整数v≥3$v\ge3$，都存在一个LRILS（v），除了v=6$v=6$。

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The spectrum for large sets of resolvable idempotent Latin squares

An idempotent Latin square of order $v$ is called resolvable and denoted by RILS(v) if the $v (v - 1)$ off-diagonal cells can be resolved into $v - 1$ disjoint transversals. A large set of resolvable idempotent Latin squares of order $v$ , briefly LRILS(v), is a collection of $v - 2$ RILS(v)s pairwise agreeing on only the main diagonal. In this article, an LRILS(v) is constructed for $v \in {14, 20, 22, 28, 34, 35, 38, 40, 42, 46, 50, 55, 62}$ by using multiplier automorphism groups. Hence, there exists an LRILS(v) for any positive integer $v \geq 3$ , except $v = 6$ .

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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.