Related papers: Meet-reducible submaximal clones determined by two…

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable \omega-categorical relational structures have two algebraic counterparts for…

There are continuum many clones on a three-element set even if they are considered up to \emph{homomorphic equivalence}. The clones we use to prove this fact are clones consisting of \emph{self-dual operations}, i.e., operations that…

For an irreducible complex character $\chi$ of the finite group $G$, let $\pi(\chi)$ denote the set of prime divisors of the degree $\chi(1)$ of $\chi$. Denote then by $\rho(G)$ the union of all the sets $\pi(\chi)$ and by $\sigma(G)$ the…

The purpose of this paper is to extend the symmetry of maximals of the ring of a germ of reducible plane curve proved by Delgado to a relation between the relative maximals of a fractional ideal and the absolute maximals of its dual for any…

We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a…

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In…

In the paper we introduce a notion of a key relation, which is similar to the notion of a critical relation introduced by Keith A.Kearnes and \'Agnes Szendrei. All clones on finite sets can be defined by only key relations. In addition…

Given an infinite set X and an ideal I of subsets of X, the set of all finitary operations on X which map all (powers of) I-small sets to I-small sets is a clone. In a 2001 article, G. Czedli and L. Heindorf asked whether or not for two…

To convert a fractional solution to an instance of a constraint satisfaction problem into a solution, a rounding scheme is needed, which can be described by a collection of symmetric operations with one of each arity. An intriguing…

Function clones are sets of functions on a fixed domain that are closed under composition and contain the projections. They carry a natural algebraic structure, provided by the laws of composition which hold in them, as well as a natural…

Given a clone C on a set A, we characterize the clone of operations on A which are local term operations of every ultrapower of the algebra $(A; C)$.

We determine all majority operations on a four-element set that generate a minimal clone.

Assuming the condition of no superluminal signalling, we got an upper bound on the quality of all asymmetric $ 1\to 2$ cloning machines, acting on qubits whose Bloch vectors lie on a great circle. Then we constructed an $ 1\to 2$ cloning…

We study clones on a four-element set related to the clone $\mathsf{DMA}$ of all term functions of the sub\-directly irreducible four-element De~Morgan algebra $\mathbf{DM_{4}}$. We find generating sets for the clones of all functions…

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…

For a class C of operations on a nonempty base set A, an operation f is called a C-subfunction of an operation g, if f = g(h_1, ..., h_n), where all the inner functions h_i are members of C. Two operations are C-equivalent if they are…

We investigate the structure of the lattice of clones on an infinite set X. We first observe that ultrafilters naturally induce clones; this yields a simple proof of Rosenberg's theorem: "there are 2^2^kappa many maximal (=precomplete)…

In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes and to multiclones. We show that every non-trivial clone contains a "small" clone of one of…

We study the most general renormalizable couplings containing Higgs $H(10)$, $D(120)$, $\overline{\Delta}(\overline{126})+ \Delta(126)$, $A(45)$, $E(54)$ and $\Phi(210)$ in the supersymmetric SO(10) models. The Clebsch-Gordan Coefficients…

We show that if $\{\rho_{\ell}\}$ is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation $\overline{\rho}_{\ell}$ is absolutely irreducible for $\ell$ in a density 1 set of…