6 citations · 20 across the 15 of their papers we have counts for
5 papers · 1 filter
Submaximal clones over a three-element set up to minor-equivalence
Albert Vucaj, Dmitriy Zhuk
We study clones modulo minor homomorphisms, which are mappings from one clone to another preserving arities of operations and respecting permutation and identification of variables…
The lattice of clones of self-dual operations collapsed
Manuel Bodirsky, Albert Vucaj, Dmitriy Zhuk
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…
Existence of cube terms in finite algebras
Alexandr Kazda, Dmitriy Zhuk
We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if su…
The Size of Generating Sets of Powers
Dmitriy Zhuk
In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. F…
Key (critical) relations preserved by a weak near-unanimity function
Dmitriy Zhuk
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 Ágnes Szendrei. All clones on finite s…