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Partial clones containing all permutations

Published online by Cambridge University Press:  17 April 2009

Lucien Haddad
Affiliation:
Département de Mathématiques et Informatique, Collége Militaire Royal du Canada, Kingston, Ontario, K7L 5L0, Canada
Ivo G. Rosenberg
Affiliation:
Département de Mathématiques et Statistique, Université de Montréal, C.P. 6128 Succ Centreville, Montréal, Qué, H3C 3J7 Canada
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Abstract

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For every nonsingleton finite set A, we construct three families of partial clones on A that contain all permutations of A and are of continuum cardinality.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Börner, F., Haddad, L. and Pöschel, R., ‘Minimal partial clones’, Bull. Austral. Math. Soc. 44 (1991), 405415.Google Scholar
[2]Freivald, R.V., ‘Completness criteria for functions of the algebra of logic and many-valued logics’, Dokl. Akad. Nauk. SSSR 6 (1966), 12491250.Google Scholar
[3]Haddad, L. and Rosenberg, I.G., ‘Maximal partial clones determined by areflexive relations’, Discrete Appl. Math. 24 (1989), 133143.Google Scholar
[4]Haddad, L. and Rosenberg, I.G., ‘Completness theory for finite partial algebras’, Algebra Universalis 29 (1992), 378401.Google Scholar
[5]Haddad, L. and Rosenberg, I.G., ‘Finite clones containing all permutations’, Canad. J. Math. 46 (1994), 951970.CrossRefGoogle Scholar
[6]Mal'tsev, A.I., ‘Iterative algebras and Post's varieties’, (in Russian), Algebra i Logika 5 (1966), 524. English translation: The metamathematics of algebraic systems, Collected papers 1936–67. Stud. Logic. Found. Math. 66, (North-Holland, 1971).Google Scholar
[7]Post, E., The two-valued iterative systems of mathematical logic, Ann. of Math. Studies 5 (Princeton University Press, Princeton, 1941).Google Scholar
[8]Romov, B.A., ‘The algebras of partial functions and their invariants’, (in Russian), Kiber-netika 2 (1981), 111. English translation: Cybernetics 17 (1981), 157–167.Google Scholar
[9]Romov, B.A., ‘Maximal subalgebras of algebras of partial multivalued logic functions’, (in Russian), Kibernatika 1 (1980), 3140. English translation, Cybernetics 16 (1980) 28–36.Google Scholar