Bezushchak D. Combinatorial Structures Related to Semigroups

The dissertation is dedicated to the study of combinatorial structures associated with semigroups. The paper explores semigroups of contracting transformations and matroids, which are generalizations of linear independence in vector spaces, examines growth issues in semigroups and Levitt algebras, and the structurality of inverse Levitt semigroups with polynomially bounded growth. The dissertation consists of abstracts in Ukrainian and English, an introduction, four main chapters, conclusions, a list of references, and an appendix. The introduction justifies the relevance of the topic, outlines the connection of the dissertation paper with scientific programs, plans, themes, specifies the aim and tasks, object, subject, and methods of research, presents the scientific novelty and practical significance of the results obtained, characterizes the personal contribution of the candidate, lists the conferences where the paper was presented, and provides a brief content of the paper. In the first chapter of the dissertation, the orders of semigroups of partially defined contracting transformations of partially ordered finite sets are calculated, and the relationship between the orders of semigroups of partially defined contracting transformations of the lexicographic and direct product of partially ordered sets with the orders of the corresponding semigroups for the components of these products is studied.