Discrete Mathematics and Applications

doi: 10.1515/dma-2025-frontmatter6pmid: N/A

Komyagin, Maksim M.

doi: 10.1515/dma-2025-0028pmid: N/A

AbstractWe study (v, k)-configurations with k = 5, which are combinatorial objects. We prove necessary and sufficient conditions for combinatorial equivalence of (v, 5)-configurations constructed from digraphs with two input and two output arcs in each vertex. We develop an algorithms for construction of (v, 5)-configurations and identification of combinatorially equivalent of (v, 5)-configurations. We also give a description of all (v, 5)-configurations for v ≤ 10 and evaluate the number of combinatorially nonequivalent (11, 5)-configurations.

Marchenkov, Sergey S.

doi: 10.1515/dma-2025-0029pmid: N/A

AbstractWe characterize the implicatively implicit extensions of all 27 two-place symmetric functions of the three-valued logic that preserve all three constants. We show that they contain extensions coinciding with the known implicatively closed classes and extensions which are not closed relative to the superposition operation.

Savelov, Maksim P.

doi: 10.1515/dma-2025-0030pmid: N/A

AbstractWe find the limit joint distribution of the statistics T1, T2, T3 of the “Monobit Test”, “Frequency Test within a Block”, and the generalized “Serial Test” tests of the NIST package in the case where the sequence under consideration consists of independent Bernoulli random variables with parameter p=12.$p=\frac{1}{2} .$ We show that T1 and (T2, T3) are asymptotically uncorrelated, T2 and T3 are asymptotically positively correlated, and T1, T2, T3 are pairwise asymptotically dependent. We also prove that the covariance matrix C of the limit distribution of the vector (T1, T2, T3) satisfies C12 = C21 = C13 = C31 = 0, C23 = C32 > 0. The limit behavior of the vector (T1, T2, T3) is described in the case p≠12.$p \neq \frac{1}{2} .$

Shchuchkin, Nikolay A.

doi: 10.1515/dma-2025-0031pmid: N/A

AbstractWe propose an algorithm for string processing which is based on finite ternary quasigroups. Ternary quasigroups are specified by three-dimensional matrices of a certain form. We prove sufficient conditions for simplicity and polynomial completeness of a finite ternary quasigroup. We also propose a method for deciding polynomial completeness of a finite ternary quasigroup based on the analysis of the corresponding three-dimensional matrix.

Sorokina, Marina M.; Nesterov, Aleksandr S.

doi: 10.1515/dma-2025-0032pmid: N/A

AbstractOnly finite groups are considered. A class of groups is called a formation if it is closed under taking homomorphic images and subdirect products. For a nonempty class Ω of simple groups, V. A. Vedernikov defined Ω-foliated formations of finite groups using two types of functions, viz., satellite functions and direction functions. Let σΩ be an arbitrary partition of the class Ω. We study σΩ-foliated formations, where σΩ is an arbitrary partition of the class Ω constructed by the authors of the preset paper as a natural generalization of the concept of an Ω-foliated formation using A. N. Skiba’s σ-methods. We prove the existence of different types of satellites of σΩ-foliated formations and describe their structure.