CEU Electronic Theses and Dissertations, 2008
| Author | Patkos, Balazs Daniel |
|---|---|
| Title | Problems in extremal finite set theory |
| Summary | In this thesis, we focus on two types of problems in extremal finite set theory. First we introduce a distance-like concept, the $\F$-free distance of two $\F$-free hypergraphs. For a fixed hypergraph $\F$, we will consider the problem of finding the pairs of hypergraphs with the largest $\F$-free distance. For some hypergraphs we will obtain exact results while for some others we will obtain upper and lower bounds on the largest $\F$-free distance. In the second part of the thesis, we will elaborate on extremal problems of weighted set systems, where the weight of a set depends only on its size. The main tool in our investigation will be the so-called profile vector of a set system and we will determine the convex hull of the profile vectors of set systems with some prescribed properties. |
| Supervisor | Katona, Gyula O.H. |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2008/tphpab01.pdf |
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