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The 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

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


Full text: PDF file (266 kB)
References: PDF file   HTML file
UDC: 519.7
MSC: 08A99,03B50

Citation: S. V. Zamaratskaya, V. I. Panteleev, “Classification and types of bases of all ultrafunctions on two-element set”, The 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 The 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 articles:
    1. S. A. Badmaev, “O klassakh bulevykh funktsii, porozhdennykh maksimalnymi chastichnymi ultraklonami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 3–14  mathnet  crossref
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