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Mathematics
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Algebra and Discrete Mathematics 2023
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Algebra and Discrete Mathematics 2023

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 5715

Special Issue Editor

Prof. Dr. Seok-Zun Song

E-Mail Website1 Website2
Guest Editor
Department of Mathematics, Jeju National University, Jeju 63243, Korea
Interests: linear operator; rank preserver; minimum permanents; BCK/BCI-algebras and related systems; fuzzy algebraic structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Algebra is a well-known research subject in the field of mathematics. Discrete mathematics is also very important subject and research area. These subjects are especially important in the development of computer science and cryptography. Thus, the aim of this Special Issue is to promote the exchange of ideas between researchers and to spread new trends in these areas. The issue is focused on all aspects of algebra, linear algebra and matrix theory, discrete mathematics and graph theory, BCK algebra and related algebraic systems, and their applications in computer sciences, informatics, decision-making problems, etc.

This Issue is a continuation of the previous successful Special Issue “Algebra and Discrete Mathematics 2021”.

Prof. Dr. Seok-Zun Song
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algebra and its applications
  • linear algebra and its applications
  • discrete mathematics
  • BCK algebras and related algebraic systems
  • (intuitionistic) fuzzy theory and applications
  • soft matrix theory and applications
  • (intuitionistic) fuzzy soft matrix theory and applications
  • neutrosophic soft matrix theory and applications
  • neutrosophic fuzzy matrix theory and applications
  • rough matrix theory and applications
  • fuzzy soft rough matrix theory and applications

Published Papers (6 papers)

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Research

17 pages, 286 KiB  
Article
New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row–Square Magic Rectangles
by Can Hu and Fengchu Pan
Mathematics 2024, 12(8), 1194; https://doi.org/10.3390/math12081194 - 16 Apr 2024
Viewed by 224
Abstract
As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem of trimagic squares with singly even [...] Read more.
As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem of trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known about the existence of trimagic squares with other even orders, except for only three examples and three families. We constructed normal trimagic squares by using product constructions, row–square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We gave a new product construction: for positive integers p, q, and r having the same parity, other than 1, 2, 3, or 6, if normal p × q and r × q row–square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we constructed normal trimagic squares of orders 8q3 and 8pqr for all odd integers q not less than 7 and p, r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
17 pages, 310 KiB  
Article
Derivations of Incidence Algebras
by Piotr Krylov and Askar Tuganbaev
Mathematics 2024, 12(7), 999; https://doi.org/10.3390/math12070999 - 27 Mar 2024
Viewed by 414
Abstract
We study the derivations of the incidence algebra I(X,R), where X is a preordered set and R is an algebra over some commutative ring T. A satisfactory description of the T-module of derivations and the [...] Read more.
We study the derivations of the incidence algebra I(X,R), where X is a preordered set and R is an algebra over some commutative ring T. A satisfactory description of the T-module of derivations and the T-module of outer derivations of this algebra is given. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
12 pages, 323 KiB  
Article
On Flag-Transitive, Point-Quasiprimitive Symmetric 2-(v,k,λ) Designs with λ Prime
by Yongli Zhang, Jiaxin Shen and Zhilin Zhang
Mathematics 2023, 11(24), 4938; https://doi.org/10.3390/math11244938 - 12 Dec 2023
Viewed by 545
Abstract
This paper contributes to the classification of flag-transitive symmetric 2-(v,k,λ) designs with λ prime. We investigate the structure of flag-transitive, point-quasiprimitive automorphism groups (G) of such 2-designs by applying the classification of quasiprimitive permutation [...] Read more.
This paper contributes to the classification of flag-transitive symmetric 2-(v,k,λ) designs with λ prime. We investigate the structure of flag-transitive, point-quasiprimitive automorphism groups (G) of such 2-designs by applying the classification of quasiprimitive permutation groups. It is shown that the automorphism groups (G) have either an abelian socle or a non-abelian simple socle. Moreover, according to the classification of finite simple groups, we demonstrate that point-quasiprimitivity implies point-primitivity of G, except when the socle of G is PSLn(q). Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
6 pages, 241 KiB  
Article
Endomorphism Type of P(3m + 1,3)
by Rui Gu and Hailong Hou
Mathematics 2023, 11(11), 2520; https://doi.org/10.3390/math11112520 - 30 May 2023
Viewed by 761
Abstract
There are six different classes of endomorphisms for a graph. The sets of these endomorphisms always form a chain under the inclusion of sets. In order to study these different endomorphisms more systematically, Böttcher and Knauer proposed the concept of the endomorphism type [...] Read more.
There are six different classes of endomorphisms for a graph. The sets of these endomorphisms always form a chain under the inclusion of sets. In order to study these different endomorphisms more systematically, Böttcher and Knauer proposed the concept of the endomorphism type of a graph in 1992. In this paper, we explore the six different classes of endomorphisms of graph P(3m+1,3). In particular, the endomorphism type of P(3m+1,3) is given. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
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46 pages, 462 KiB  
Article
Cohomology Algebras of a Family of DG Skew Polynomial Algebras
by Xuefeng Mao and Gui Ren
Mathematics 2023, 11(7), 1617; https://doi.org/10.3390/math11071617 - 27 Mar 2023
Cited by 1 | Viewed by 1540
Abstract
Let A be a connected cochain DG algebra such that its underlying graded algebra A# is the graded skew polynomial algebra [...] Read more.
Let A be a connected cochain DG algebra such that its underlying graded algebra A# is the graded skew polynomial algebra k⟨x1,x2,x3⟩/x1x2+x2x1x2x3+x3x2x3x1+x1x3,|x1|=|x2|=|x3|=1. Then the differential ∂A is determined by ∂A(x1)∂A(x2)∂A(x3)=Mx12x22x32 for some M∈M3(k). When the rank r(M) of M belongs to {1,2,3}, we compute H(A) case by case. The computational results in this paper give substantial support for the research of the various homological properties of such DG algebras. We find some examples, which indicate that the cohomology graded algebras of such kind of DG algebras may be not left (right) Gorenstein. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
23 pages, 312 KiB  
Article
On the Construction of Pandiagonal Magic Cubes
by Fucheng Liao and Hao Xie
Mathematics 2023, 11(5), 1185; https://doi.org/10.3390/math11051185 - 28 Feb 2023
Viewed by 1298
Abstract
This paper investigates the construction method of pandiagonal magic cube. First, we define a pandiagonal Latin cube. According to this definition, the cube can be constructed by simple methods. After designing a set of orthogonal pandiagonal Latin cubes, the corresponding order pandiagonal magic [...] Read more.
This paper investigates the construction method of pandiagonal magic cube. First, we define a pandiagonal Latin cube. According to this definition, the cube can be constructed by simple methods. After designing a set of orthogonal pandiagonal Latin cubes, the corresponding order pandiagonal magic cube can be constructed. In addition, we give the algebraic conditions of the universal diagonal Latin cube orthogonality and the strict theoretical proof. Based on the proposed method, it can be shown that at least 6(n!)3 pandiagonal magic cubes of order n is formed through a pandiagonal Latin cube. Moreover, our method is easy to implement by computer program. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)
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