Reference : Relation graphs and partial clones on a 2-element set.
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Physical, chemical, mathematical & earth Sciences : Mathematics
Relation graphs and partial clones on a 2-element set.
Schölzel, Karsten mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Couceiro, Miguel [Université Paris Dauphine, Paris, France]
Haddad, Lucien [Royal Military College of Canada]
Waldhauser, Tamás [University of Szeged, Szeged, Hungary]
Multiple-Valued Logic (ISMVL), 2014 IEEE 44rd International Symposium on
ISMVL 2014 IEEE International Symposium on Multiple-Valued Logic
19-05-2014 to 21-05-2014
[en] Partial clones ; Representing relations by graphs ; Lattice isomorphisms
[en] In a recent paper, the authors show that the sublattice of partial clones that preserve the relation $\{(0,0),(0,1),(1,0)\}$ is of continuum cardinality on $\2$.
In this paper we give an alternative proof to this result by making use of a representation of relations derived from $\{(0,0),(0,1),(1,0)\}$ in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones.

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