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Mathematics
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Theory and Application of Algebraic Combinatorics, 2nd Edition
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Theory and Application of Algebraic Combinatorics, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1835

Special Issue Editors

Dr. Nikolai Manev

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Guest Editor
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria
Interests: coding theory; cryptography; algebra; combinatorics
Special Issues, Collections and Topics in MDPI journals
Dr. Silvia Boumova

E-Mail Website
Guest Editor
Faculty of Mathematics and Informatics, Sofia University, 1504 Sofia, Bulgaria
Interests: free associative algebra; noncommutative invariant theory; symmetric polynomials; finitely generated algebra
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Svetlana Topalova

E-Mail Website
Guest Editor
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria
Interests: combinatorial designs and their resolutions; coding theory; cryptography; computer-aided classification of combinatorial structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Algebraic combinatorics has a long history but still remains a dynamic and fascinating research area. It is a multidisciplinary area due to its overlap with other branches of mathematics. Many results and methods of algebraic combinatorics can be observed in proofs in other research areas. For example, the difficulties that must be overcome in algebra and discrete mathematics quite often have a combinatorial character.

This Special Issue entitled “Theory and Application of Algebraic Combinatorics, 2nd Edition” aims to publish papers with new results in either specific problems of algebraic combinatorics or those that demonstrate their relationships with other mathematical areas.

Potential topics of this Special Issue include, but are not limited to, the following:

  • Orthogonal arrays and their generalizations;
  • Enumeration problems, power series, and generating functions;
  • Automorphism groups of finite structures and codes;
  • Finite projective space;
  • Projective Hjelmslev geometries and codes over finite chain rings;
  • Free associative algebras over fields with a positive characteristic;
  • Non-commutative invariant theory;
  • Algebraic curves over finite fields;
  • Error-correcting codes, network coding, and optical orthogonal codes;
  • Algorithms and software tools for algebraic combinatorics, coding theory, and cryptography.

Dr. Nikolai Manev
Dr. Silvia Boumova
Prof. Dr. Svetlana Topalova
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 250 words) can be sent to the Editorial Office for assessment.

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

  • orthogonal arrays
  • parallelisms of finite projective space
  • finite structures and codes
  • arcs in projective geometries
  • Hjelmslev geometries
  • automorphism groups
  • codes over finite chain rings
  • symmetric and alternative polynomials
  • finitely generated algebras
  • young tableau
  • code division multiple access systems

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Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (2 papers)

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Research

12 pages, 260 KB  
Article
Certain Mathematical Constants Associated with Harmonic Numbers and Higher-Dimensional Harmonic Sums
by Junesang Choi
Mathematics 2026, 14(6), 962; https://doi.org/10.3390/math14060962 - 12 Mar 2026
Viewed by 601
Abstract
The Euler–Mascheroni constant γ, defined as the limiting difference between the harmonic numbers Hn and logn, has long been studied and appears in diverse areas of number theory, analysis, and special functions. In this paper, we establish a unified [...] Read more.
The Euler–Mascheroni constant γ, defined as the limiting difference between the harmonic numbers Hn and logn, has long been studied and appears in diverse areas of number theory, analysis, and special functions. In this paper, we establish a unified formula for (k+1)-fold harmonic sums expressed in terms of harmonic numbers. Several particular cases are examined in detail, and their asymptotic expansions are derived, leading to the identification of both classical and additional limiting constants. These results place higher-order harmonic sums within a common analytic framework and clarify the structure of their normalized limits. The broader mathematical significance of the additional constants arising from this approach remains to be determined and may warrant further investigation. Full article
(This article belongs to the Special Issue Theory and Application of Algebraic Combinatorics, 2nd Edition)
9 pages, 250 KB  
Article
Counting Rainbow Solutions of a Linear Equation over Fp via Fourier-Analytic Methods
by Francisco-Javier Soto
Mathematics 2025, 13(21), 3374; https://doi.org/10.3390/math13213374 - 23 Oct 2025
Viewed by 657
Abstract
We study rainbow solutions to linear equations modulo a prime p, where the residue classes are partitioned into n color classes. Using the Fourier method, we derive a universal lower bound that depends only on the class densities and a single spectral [...] Read more.
We study rainbow solutions to linear equations modulo a prime p, where the residue classes are partitioned into n color classes. Using the Fourier method, we derive a universal lower bound that depends only on the class densities and a single spectral parameter: the Fourier bias (the largest nontrivial Fourier coefficient) of each class. When the biases are at the square-root cancellation scale p−1/2 (for random colorings, up to a logp factor), the bound recovers the optimal growth pn−1 with an explicit leading constant and negligible error. Our results complement recent work: in low-bias regimes (pseudorandom or random) they yield sharper quantitative bounds with transparent constants, and the bound requires no extra hypotheses such as coefficient separability. Full article
(This article belongs to the Special Issue Theory and Application of Algebraic Combinatorics, 2nd Edition)
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