Minimal clones generated by majority operations

A complete classification of Constraint Languages generated by binary entropic minimal clones

While finishing this paper I found the paper [9] which proves that a binary operation that is generates a minimal clone is NP-complete is the operation is non-commutative and is polynomial if the operation is equivalent to a commutative operation that generates the clone. From this result all results in this paper can be (even more) trivially proved. This paper might be of interest to some read...

Clones with Nullary Operations

This article discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary sets. By means of two pairs of kernel and closure operators, the relationship between such clones and clones in the traditional sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. Finall...

On Some Clones of Compatible Operations

In [5], new results on affine complete algebras are obtained using the formalism of generalized metric spaces introduced by Jawhari, Misane and Pouzet [3]. In this paper we focus our attention to the clones of compatible operations obtained by the mean of nonexpansive functions defined on a generalized metric space. We hence prove new results on relations and primal algebras. We apply the notio...

A note on clones with nullary operations

The Minimal Clones above the Permutations

We determine the atoms of the interval of the clone lattice consisting of those clones which contain all permutations, on an infinite base set. This is equivalent to the description of the atoms of the lattice of transformation monoids above the permutations. 1. The problem and the result Let X be an infinite set of cardinality κ = אα, let O be the set of all finitary operations on X, and for a...