The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-202102124020 |
| Date | 12 February 2021 |
| Creators | Hong Ngoc, Binh |
| Contributors | Prof. Dr. Matthias Reitzner, Prof. Dr. Ngo Viet Trung |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, application/zip |
| Rights | Attribution-NonCommercial-ShareAlike 4.0 International, http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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