Ars Combinatoria

ISSN 0381-7032 (print), 2817-5204 (online)

Ars Combinatoria is the oldest Canadian journal of combinatorics, established in 1976, dedicated to advancing combinatorial mathematics through the publication of high-quality, peer-reviewed research papers. Over the decades, it has built a strong international reputation and continues to serve as a leading platform for significant contributions to the field.
Open Access:  The journal follows the Diamond Open Access model—completely free for both authors and readers, with no article processing charges (APCs). 
Publication Frequency: From 2024 onward, Ars Combinatoria publishes four issues annually—in March, June, September, and December.
Scope: Publishes research in all areas of combinatorics, including graph theory, design theory, enumeration, algebraic combinatorics, combinatorial optimization and related fields.
Indexing & Abstracting:  Indexed in MathSciNet, Zentralblatt MATH, and EBSCO, ensuring wide visibility and scholarly reach.
Rapid Publication: Submissions are processed efficiently, with accepted papers published promptly in the next available issue.
Print & Online Editions: Issues are available in both print and online formats to serve a broad readership.

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On the Existence of \((v,4, 1)\)-PMD

Zhang Xuebin1
1Department of Mathematics Suzhou University, Suzhou People’s Republic of China
Abstract:

FE. Bennett has proved that a \((v, 4, 1)\)-RPMD exists for every positive integer \(v \equiv 1 \pmod{4}\) with the possible exception of \(v = 33, 57, 93\) and \(133\). In this paper, we shall first introduce the concept of an incomplete PMD and use it to establish some construction methods for Mendelsohn designs; then we shall give the following results: (1) a \((v, 4, 1)\)-PMD exists for every positive integer \(v \equiv 0 \pmod{4}\) with the exception of \(v = 4\) and the possible exception of \(v = 8, 12\);(2) a \((v, 4, 1)\)-PMD exists if \(v = 57, 93\) or \(133\).

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