Abstract
The closed class
Funding statement: Research was supported by Ministry of Science and Higher Education of the Russian Federation within the framework of the program of Moscow Center of Fundamental and Applied Mathematics under the Agreement 075-15-2022-284.
Acknowledgement
The author thanks Prof. V. B. Alekseev for fruitful discussion of the paper and valuable questions and comments on it.
References
[1] Yablonskij S. V., “Functional constructions in a k-valued logic”, Tr. Mat. Inst. Steklova, 51 (1958), 5–142 (in Russian).Suche in Google Scholar
[2] Ayzenberg N. N., Semyon I. V., “Some criteria for the representability of functions of k-valued logic by polynomials modulo k”, Multi-resistant elements and their application, M.: Sov. radio, 1971, 84–88 (in Russian).Suche in Google Scholar
[3] Cherepov A. N., “Description of the structure of closed classes in Pk containing the class of polynomials”, Problems of Cybernetics, 40, M.: Nauka, 1983, 5–18 (in Russian).Suche in Google Scholar
[4] Remizov A. V., “Superstructure of the closed class of polynomials modulo k”, Discrete Math. Appl., 1:1 (1991), 9–22.10.1515/dma.1991.1.1.9Suche in Google Scholar
[5] Meshchaninov D. G., “A method for constructing polynomials of k-valued logic functions”, Discrete Math. Appl., 5:4 (1995), 333–346.10.1515/dma.1995.5.4.333Suche in Google Scholar
[6] Krokhin A. A., Safin K. L., Sukhanov E. V., “On the structure of the lattice of closed classes of polynomials”, Discrete Math. Appl., 7:2 (1997), 131–146.10.1515/dma.1997.7.2.131Suche in Google Scholar
[7] Selezneva S. N., “On the number of polynomial functions of k-valued logic modulo a composite k”, Discrete Math. Appl., 27:1 (2017), 7–14.10.1515/dma-2017-0002Suche in Google Scholar
[8] Meshchaninov D. G., “Closed classes of polynomials modulo p2”, Discrete Math. Appl., 28:3 (2018), 167–178.10.1515/dma-2018-0016Suche in Google Scholar
[9] Meshchaninov D. G., “Some families of closed classes in Pk defined by additive formulas”, Discrete Math. Appl., 32:2 (2022), 115–128.10.1515/dma-2022-0011Suche in Google Scholar
[10] Alekseev V. B., “On closed classes in partial k-valued logic that contain all polynomials”, Discrete Math. Appl., 31:4 (2021), 231–240.10.1515/dma-2021-0020Suche in Google Scholar
[11] Alekseev V. B., “On the cardinality of interval Int(Polk) in partial k-valued logic”, Moscow University Mathematics Bulletin, 77:3 (2022), 120–126.10.3103/S0027132222030032Suche in Google Scholar
[12] Marchenkov S. S., Functional systems with superposition operation, M.: Fizmatlit, 2004 (in Russian), 104 pp.Suche in Google Scholar
[13] Lau D., Function Algebras on Finite Sets, Springer, 2006, 671 pp.Suche in Google Scholar
[14] Carlitz L., “Functions and polynomials (mod pn)”, Acta Arithmetica, IX (1964), 67–78.10.4064/aa-9-1-67-78Suche in Google Scholar
[15] Gavrilov G. P., Sapozhenko A. A., Problems and exercises in discrete mathematics, M.: Fizmatlit, 2004 (in Russian), 416 pp.Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation
Artikel in diesem Heft
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation