|
|
Minion Cores of Clones
Kapytka, Maryia ; Barto, Libor (advisor) ; Zhuk, Dmitrii (referee)
This thesis provides a classification of the minion homomorphism preordering and minion cores within a class of multi-sorted Boolean clones. These clones can be described as those clones defined on the set {0, 1}k = {0, 1} × {0, 1} × · · · × {0, 1}, where the clone operations act component-wise on the k-tuples, which are determined by multi-sorted unary or binary relations. The second chapter of this thesis focuses on presenting the key findings. We introduce specific minion cores and establish the preordering among them. Furthermore, we prove that each clone falling under the aforementioned type is equivalent to one of these minion cores.
|
|
| |
|
|
The Number of Homomorphisms to a Fixed Algebra
Kapytka, Maryia ; Barto, Libor (advisor) ; Stanovský, David (referee)
In this work we give a partial answer to the following question: For which fixed finite algebras A is the number of homomorphisms from a similar algebra X to A bounded from above by a polynomial in the size of X? The work is divided into two parts: Preliminaries and Results. In the first part we introduce the reader to this topic and give some basic facts about the number of homomorphisms. In the main part we generalize the case of a two-element semilattice to a general finite semilattice, then we look at a specific three- element algebra with a majority operation and a specific three-element 2-semilattice, the rock-paper-scissors algebra. Then we study groups. Finally we consider unary algebras. All the algebras mentioned above apart from unary algebras give a positive answer to our question. 1
|
guest ::
