Toward a Solution of Archdeacon's Conjecture on Integer Heffter Arrays

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2025-05-20 DOI:10.1002/jcd.21983

Marco Antonio Pellegrini, Tommaso Traetta

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引用次数: 0

Abstract

In this article, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays $H (m, n; s, k)$ whenever the necessary conditions hold, that is, $3 ⩽ s ⩽ n$ , $3 ⩽ k ⩽ m$ , $m s = n k$ and $n k \equiv 0, 3 (\mod 4)$ . By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever $k ⩾ 7 \cdot gcd (s, k)$ is odd and $s \neq 3, 5, 6, 10$ .

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关于整数Heffter数组上Archdeacon猜想的一个解

在本文中，我们对Dan Archdeacon关于整数Heffter数组H (m，n ;S, k)，即，3±s±n；3±k±m；M s = n k和nK≡0，3 （mod 4）。通过构造整数Heffter数组集，每当k大于或等于7·GCD (年代 ,K)是奇数且s≠3，5、6、10。

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.