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A Note on Counting Basic Choice Functions with Formal Concept Analysis
P. 47–56.
The paper aims at not only counting how many basic choice functions exist on a finite set of alternatives (all, non-empty, single-element valued) but shows how to do this with the help of Formal Concept Analysis. Moreover, we introduce the contextual representation of a choice function by considering the formal context of its map from 2 𝐴 to 2 𝐴 . We also characterise these contexts as nominal scales of a certain size and build a lattice of all choice functions with their help. Last but not least, we study the asymptotic behaviour of those obtained and new counting formulas that do not have a closed form.
Publication based on the results of:
In book
Vol. 3489. , CEUR-WS.org, 2023.
Ignatov D. I., , in: 11th International Conference, AIST 2023, Yerevan, Armenia, September 28–30, 2023, Revised Selected Papers. Analysis of Images, Social Networks and Texts. Lecture Notes in Computer Science (LNCS, volume 14486).: Cham: Springer, 2024. P. 349 – 361.
This paper dates back to the asymptotic solutions of Rota’s problem on the size of maximum antichain in the set partition lattice by Canfield and Harper and others. The knowledge of asymptotic coefficients could pave the way to the asymptotic solutions of such problems as (maximal) antichain counting in partition lattices. In addition to our ...
Added: January 23, 2026
Springer, 2025.
The second edition of this 5-volume handbook is intended to be a basic yet comprehensive reference work in combinatorial optimization that will benefit newcomers and researchers for years to come. This multi-volume work deals with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The editors have brought together almost every aspect ...
Added: January 18, 2026
Елохин А. А., / Series math-ph "Mathematical Physics". 2025.
In rigorous study of stochastic models for the wave turbulence theory and R. Peierls's kinetic theory for the thermal conductivity in solids, analysis of integrals of the form $\int_{\mathcal{M}}\frac{F\omega_\mathcal{M}}{\Omega^2 + \nu^2\Gamma^2}$ and $\int_{\mathcal{M}}\frac{F\cos(\nu^{-1}\Omega)\omega_\mathcal{M}}{\Omega^2 + \nu^2\Gamma^2}$ plays a crucial role, where $\nu>0$ is a small parameter, $\mathcal{M}$ is a closed Riemannian manifold with volume form $\omega_\mathcal{M}$, ...
Added: September 30, 2025
Bille A., Buchstaber V., Coste S. et al., Journal of Physics A: Mathematical and Theoretical 2025 Vol. 58 No. 2 Article 025212
We analyze the numbers of closed paths of length on two important regular lattices: the hexagonal lattice (also called graphene in chemistry) and its dual triangular lattice. These numbers form a moment sequence of specific random variables connected to the distance of a position of a planar random flight (in three steps) from the origin. Here, we refer to such ...
Added: August 22, 2025
Khestanov R., Suvalko A., Социологическое обозрение 2025 Т. 24 № 2 С. 164–189
The article examines the genesis of the concept of novelty and argues that modern difficulties in defining and identifying the new are a symptom of a semantic crisis, which is based on the loss of strategic normativity of novelty in modern culture. Three historical-semantic models of novelty are identified and analyzed: cyclical (characteristic of prehistoric ...
Added: June 29, 2025
М.: Математический институт им. В. А. Стеклова РАН, 2024.
This volume is dedicated to the 80th birthday of Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences. The volume includes articles on topology, geometry, combinatorics, and mathematical physics, the areas in which V. M. Buchstaber is a recognized world leader and the head of an active scientific school. Most of the articles are written ...
Added: January 15, 2025
Providence: AMS, 2023.
This book is a translation from Russian of Part III of the book Mathematics via Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, and Part II, Geometry, have been published in the same series.
The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences ...
Added: March 3, 2024
Galitsky B., Ilvovsky D., Goncharova E., , in: Proceedings of the 10th International Workshop "What can FCA do for Artificial Intelligence?"Vol. 3233.: CEUR Workshop Proceedings, 2022. P. 75–87.
Supported decision trees that have been first proposed to boost the performance and the explainability of the expert systems built upon the texts can become a great basis for the machine reading comprehension (MRC) systems. The supported decision tree is based on building and combining the corresponding discourse trees for the text passage. In this work, ...
Added: November 1, 2022
Beisegel J., Chudnovsky M., Gurvich V. et al., , in: Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer ScienceVol. 11646.: Springer, 2019. P. 126–139.
A vertex v in a graph G is said to be avoidable if every induced two-edge path with midpoint v is contained in an induced cycle. Generalizing Dirac’s theorem on the existence of simplicial vertices in chordal graphs, Ohtsuki et al. proved in 1976 that every graph has an avoidable vertex. In a different generalization, Chvátal et al. gave in 2002 a characterization of graphs ...
Added: October 26, 2021
Koroleva Y., Wall P., Fabricius J., Asymptotic Analysis 2013 Vol. 84 No. 1-2 P. 103–121
We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the ...
Added: October 18, 2021
Cham: Birkhäuser, 2021.
Is published at every edition of EuroComb which is one of the leading conferences in the area worldwide
Presents the most recent achievements in this conference
Collects the extended abstracts of the accepted contributions to EuroComb21 ...
Added: September 8, 2021
Боровков А. А., Cambridge University Press, 2020.
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established ...
Added: March 30, 2021
Springer, 2020.
This book constitutes the proceedings of the 15th International Computer Science Symposium in Russia, CSR 2020, held in Yekaterinburg, Russia, in June 2020.
The 25 full papers and 6 invited papers were carefully reviewed and selected from 49 submissions. The papers cover a broad range of topics, such as: algorithms and data structures; computational complexity, including ...
Added: September 4, 2020
Chistikov D., Mikhail Vyalyi, , in: LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science. Saarbrücken, Germany. July, 2020.: Association for Computing Machinery (ACM), 2020. P. 312–326.
Added: September 4, 2020
М.: Изд-во механико-математического факультета МГУ, 2019.
Сборник содержит материалы XII Международного семинара «Дискретная математика и ее приложения» имени академика О.Б. Лупанова, проходившего на механико-математическом факультете МГУ имени М. В. Ломоносова с 17 по 22 июня 2019 г. при поддержке Российского фонда фундаментальных исследований (проект 16–01–20345). Семинар охватывает следующие направления в области дискретной математики: теория функциональных систем, синтез, сложность и надежность управляющих ...
Added: October 17, 2019
Polyakov N. L., Shamolin M. V., Doklady Mathematics 2014 Vol. 89 No. 3 P. 290–292
A complete classification of symmetric sets of choice functions with the Arrow property is obtained. ...
Added: October 5, 2018
Avdoshin S. M., Набебин А. А., М.: ДМК Пресс, 2019.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite ...
Added: August 24, 2018