Unique inclusions of maximal C-clones in maximal clones

C-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in work by Creignou et al. from 2008 . We completely describe the relationship regarding set inclusion between maxim...

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Bibliographic Details
Published in:Algebra universalis 2018-06, Vol.79 (2), p.1-21, Article 31
Main Authors: Behrisch, Mike, Vargas-García, Edith
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Polymorphism
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Summary:C-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in work by Creignou et al. from 2008 . We completely describe the relationship regarding set inclusion between maximal C-clones and maximal clones. As a main result we obtain that for every maximal C-clone there exists exactly one maximal clone in which it is contained. A precise description of this unique maximal clone, as well as a corresponding completeness criterion for C-clones is given.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-018-0497-9