Geodesic
On Some Closed Classes of Self-dual Partial Many-valued Functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 16-24

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Let $S$ be a class of fully defined functions of any number of variables that are defined and take values in the set $E_k=\{0,1,\dots,k-1\}$ and are self-dual under given permutation on $E_k$. Let $S^*$ be the set of all partially defined $k$-valued functions that can be extended to functions from $S$. In this paper all closed classes (under superposition) that contain $S$ and are contained in $S^*$ are described for the case when permutation is the product of non-intersecting cycles of the same length.
Keywords: $k$-valued function, partially defined function, closed class, self-dual function. 
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     author = {V. B. Alekseev},
     title = {On {Some} {Closed} {Classes} of {Self-dual} {Partial} {Many-valued} {Functions}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {16--24},
     publisher = {mathdoc},
     volume = {151},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/}
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V. B. Alekseev. On Some Closed Classes of Self-dual Partial Many-valued Functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 16-24. http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a2/