Oldal címe
Hypercycle systems
Címlapos tartalom
The aim of this research is to find constructions in hypergraphs, that are relevant from a design theoretic point of view.
The project is working on finding C (r, k, v) hypercycle systems. In this work, the term k-cycle is used in the sense of tight k-cycle, which means a cyclic sequence of k vertices and k hyperedges formed by the r-tuples of consecutive vertices.
As a relative of Steiner systems, a hypercycle system C (r, k, v) of order v is a family C of k-cycles such that each edge of the complete r-uniform hypergraph with v vertices is contained in precisely one k-cycle of C . This project analyzes the existence of C (3, k, v) hypercycle systems, focusing on special structured versions, namely cyclic and cyclic 2-split systems.
Combinatorial designs have a huge number of applications in various fields, e.g. in statistical experimental design, coding theory, optical networks, and even in music composition.