Let M be a finite set of random uniformly distributed points lying in a unit cube. Every four points from M make a tetrahedron and the tetrahedron can either contain some of the other points from M, or it can be empty. This diploma thesis brings an upper bound of the expected value of the number of empty tetrahedra with respect to size of M. We also show how precise is the upper bound in comparison to an approximation computed by a straightforward algorithm. In the last section we move from the three- dimensional case to a general dimension d. In the general d-dimensional case we have empty d-simplices in a d-hypercube instead of empty tetrahedra in a cube. Then we compare the upper bound for d-dimensional case to the results from another paper on this topic. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:435091 |
| Date | January 2020 |
| Creators | Reichel, Tomáš |
| Contributors | Valtr, Pavel, Balko, Martin |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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