Unique inclusions of maximal C-clones in maximal clones

Behrisch, Mike; Vargas García, Edith Mireya

doi:10.1007/s00012-018-0497-9

Record link:

http://hdl.handle.net/20.500.12708/85

Title:

Unique inclusions of maximal C-clones in maximal clones

Citation:

Behrisch, M., & Vargas García, E. M. (2018). Unique inclusions of maximal C-clones in maximal clones. Algebra Universalis, 79, 1–21. https://doi.org/10.1007/s00012-018-0497-9

Publisher DOI:

10.1007/s00012-018-0497-9

CatalogPlus:

AC15321022

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Behrisch, Mike
Vargas García, Edith Mireya

Organisational Unit:

E104 - Institut für Diskrete Mathematik und Geometrie

Journal:

Algebra Universalis

ISSN:

0002-5240

Date (published):

20-Apr-2018

Number of Pages:

Publisher:

SPRINGER BASEL AG

Peer reviewed:

Yes

Keywords:

Clone; C-clone; Clausal relation; Maximal C-clone; Maximal clone

Abstract:

C-clones are polymorphism sets of so-called clausal relations, aspecial type of relations on a finite domain, which first appeared in con-nection with constraint satisfaction problems in work by Creignou et al.from2008. We completely describe the relationship regarding set inclu-sion between maximal C-clones and maximal clones. As a main result weobtain that for every maximal C-clone there exists exactly one maximalclone in which it is contained. A precise description of this unique maxi-mal clone, as well as a corresponding completeness criterion for C-clonesis given.

License:

CC BY 4.0