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AppliedMath
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Algebraic Combinatorics in Data Science and Optimisation
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Algebraic Combinatorics in Data Science and Optimisation

A special issue of AppliedMath (ISSN 2673-9909).

Deadline for manuscript submissions: 31 July 2025 | Viewed by 1425

Special Issue Editor

Prof. Dr. Takayuki Hibi

E-Mail Website
Guest Editor
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita 565-0871, Osaka, Japan
Interests: computational commutative algebra; discrete mathematics; combinatorics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, data science and optimization are attractive fields. There is no doubt that algebraic and combinatorial methods are extremely useful in this research field. Combinatorics, on the other hand, is a broad field, and algebraic combinatorics in particular has made tremendous progress over the past quarter century and continues to develop as a research field that organically links combinatorics and various branches of algebra. This Special Issue aims to capture the shades of algebraic combinatorics that emerge in data science and optimization research to provide new topics in algebraic combinatorics from the perspective of applied mathematics, and to give birth to a novel trend in algebraic combinatorics.

Prof. Dr. Takayuki Hibi
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. AppliedMath is an international peer-reviewed open access quarterly 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 1200 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

  • convex polytope
  • finite partially ordered set
  • finite graph
  • simplicial complex
  • statistics
  • experimental design
  • business acumen
  • communication
  • databases
  • marketing
  • discrete optimization
  • linear programming
  • integer programming
  • machine learning

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Published Papers (2 papers)

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Research

30 pages, 1477 KiB  
Article
Algebraic Combinatorics in Financial Data Analysis: Modeling Sovereign Credit Ratings for Greece and the Athens Stock Exchange General Index
by Georgios Angelidis and Vasilios Margaris
AppliedMath 2025, 5(3), 90; https://doi.org/10.3390/appliedmath5030090 - 15 Jul 2025
Viewed by 109
Abstract
This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence on financial markets remains contested. This research adopts a [...] Read more.
This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence on financial markets remains contested. This research adopts a multi-method analytical framework combining algebraic combinatorics and time-series econometrics. The methodology incorporates the construction of a directed credit rating transition graph, the partially ordered set representation of rating hierarchies, rolling-window correlation analysis, Granger causality testing, event study evaluation, and the formulation of a reward matrix with optimal rating path optimization. Empirical results indicate that credit rating announcements in Greece exert only modest short-term effects on the Athens Stock Exchange General Index, implying that markets often anticipate these changes. In contrast, sequential downgrade trajectories elicit more pronounced and persistent market responses. The reward matrix and path optimization approach reveal structured investor behavior that is sensitive to the cumulative pattern of rating changes. These findings offer a more nuanced interpretation of how sovereign credit risk is processed and priced in transparent and fiscally disciplined environments. By bridging network-based algebraic structures and economic data science, the study contributes a novel methodology for understanding systemic financial signals within sovereign credit systems. Full article
(This article belongs to the Special Issue Algebraic Combinatorics in Data Science and Optimisation)
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21 pages, 581 KiB  
Article
The Search-o-Sort Theory
by Anurag Dutta, Sanjeev Kumar, Deepkiran Munjal and Pijush Kanti Kumar
AppliedMath 2025, 5(2), 64; https://doi.org/10.3390/appliedmath5020064 - 29 May 2025
Cited by 1 | Viewed by 479
Abstract
In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time [...] Read more.
In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time Ox2, and in the optimized cases, they take linearithmic time Ox·logx, with no existing method surpass this lower bound, given arbitrary data, i.e., ordering a list of cardinality x in Ox·logx−ϵ(x)∀ϵ(x)>0. This research proposes Search-o-Sort, which reinterprets sorting in terms of searching, thereby offering a new framework for ordering arbitrary data. The framework is applied to classical search algorithms,–Linear Search, Binary Search (in general, k-ary Search), and extended to more optimized methods such as Interpolation and Jump Search. The analysis suggests theoretical pathways to reduce the computational complexity of sorting algorithms, thus enabling algorithmic development based on the proposed viewpoint. Full article
(This article belongs to the Special Issue Algebraic Combinatorics in Data Science and Optimisation)
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