Symmetries in Algebraic Combinatorics and Their Applications
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: 31 August 2026 | Viewed by 7
Special Issue Editors
Interests: representation of algebras and its applications; algebraic combinatorics; cryptography
Interests: algebra; ring theory; Specht problem; combinatorial geometry; affine algebraic geometry
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
This Special Issue is devoted to the successful integration of combinatorics and algebra, which allows us to find deep results across a wide variety of topics. For instance, the role of graph theory in the research on associative and non-associative algebras and group theory is remarkable.
Catalan combinatorics, realized by Dyck paths, integer friezes, binary trees, and polygon triangulations, have been helpful in studying Dynkin algebras, Thompson’s groups, and cluster algebras.
Cayley graphs, nilpotent graphs, snake graphs, and posets have had a significant role in group theory, ring theory, and cluster algebras, which have a strong relationship with combinatorics, rational knots, and the theory of the representation of algebras. In particular, the perfect matching of certain graphs can be used to define quantum entanglement states, and the perfect matching of snake graphs can be used to define string modules and cluster variables associated with some cluster algebras. Furthermore, Ferrers graphs, integer partitions, multisets, and posets are appropriate tools for studying seaweed Lie algebras, Gelfand–Tsetlin modules, finite groups, branched coverings, Brauer configuration algebras, the theory of the representation of algebras, and matrix problems.
The interplay between combinatorics and algebra has applications in supercomputer designs, cryptography, cybersecurity, topological and Brauer data analysis, artificial intelligence, and quantum computing.
This Special Issue aims to encourage researchers interested in the interplay between algebra, combinatorics, and their applications to publish their results on these topics.
This Special Issue will publish full and survey papers related to, but not limited to, the following subjects:
- Cayley graphs, their relationships with group theory, and their cryptography and computer design applications.
- Nilpotent graphs and their relationships with ring theory.
- Snake graphs and their relationships with Diophantine analysis, cluster algebras, and rational knots.
- Perfect matchings and their relationships with number theory and quantum computing.
- Integer partitions and their relationships with Lie algebras, Brauer configuration algebras, and group theory.
- Poset representations and their relationships with quiver representations.
- Catalan combinatorics and its relationships with Thompson's groups and the theory of the representation of algebras.
- Applications of the interplay between combinatorics and algebra in quantum computing and topological and Brauer data analysis.
Prof. Dr. Agustín Moreno Cañadas
Prof. Dr. Alexei Kanel-Belov
Guest Editors
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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
- Cayley graph
- binary tree
- Dyck path
- Christoffel word
- integer frieze
- integer partition
- nilpotent graph
- prime graph
- polygon triangulation
- poset
- snake graph
- braid representation
- Dynkin algebra
- cluster algebra
- Lie algebra
- matrix problem
- poset representation
- quiver representation
- Thompson’s group
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.
Further information on MDPI's Special Issue policies can be found here.
