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Bulletin of Irkutsk State University. Series Mathematics, 2016, Volume 16, Pages 58–70 (Mi iigum261)  
This article is cited in 1 scientific paper (total in 1 paper)

Classification and types of bases of all ultrafunctions on two-element set

S. V. Zamaratskayaa, V. I. Panteleevb

a Medical Information-Analytic Center of Irkutsk Region, 2, Kalandarishvili, Irkutsk, 664011
b Irkutsk State University, 1, K. Marx st., Irkutsk, 664003
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Abstract: This paper studies properties of ultrafunctions with respect of their inclusion in maximal clones.
The number of maximal clones for all ultrafunctions of rank 2 is equal to 11 [V. Panteleev, 2009].
All ultrafunctions are divided into 45 equivalence classes.
Based on this classification all kinds of bases are discribed. Two bases are of different kinds if there is a function in one basis with no equivalent function in the other one. We show that bases of hyperfunctions can have cardinality from 1 to 4: there is only one kind of basis with cardinality 1, 180 with cardinality 2, 686 with cardinality 3, 28 with cardinality 4.
Keywords: ultrafunction, clone, base, maximal clone.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00621_а
Document Type: Article
UDC: 519.7
MSC: 08A99,03B50
Language: Russian
Citation: S. V. Zamaratskaya, V. I. Panteleev, “Classification and types of bases of all ultrafunctions on two-element set”, Bulletin of Irkutsk State University. Series Mathematics, 16 (2016), 58–70
Citation in format AMSBIB
\Bibitem{ZamPan16}
\by S.~V.~Zamaratskaya, V.~I.~Panteleev
\paper Classification and types of bases of all ultrafunctions on two-element set
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2016
\vol 16
\pages 58--70
\mathnet{http://mi.mathnet.ru/iigum261}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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