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dc.contributor.supervisorPrymak, Andriy
dc.contributor.authorDiao, Mingyang
dc.date.accessioned2022-03-31T20:04:54Z
dc.date.available2022-03-31T20:04:54Z
dc.date.copyright2022-03-16
dc.date.issued2022-03-16
dc.date.submitted2022-03-17T04:00:47Zen_US
dc.identifier.urihttp://hdl.handle.net/1993/36378
dc.description.abstractWe denote by $H_n$ the minimum number such that any convex body in $\mathbb{R}^{n}$ can be covered by $H_n$ of its smaller homothets. Considering an $n$-dimensional cube, one can easily see that $H_n\geqslant2^{n}$. It is a well-known conjecture that $H_n= 2^{n}$ for all $n\geqslant 3$. The main result of this thesis is the inequalities $H_5\leqslant 1002$ and $H_6\leqslant 14140$. The previously known upper bounds were $H_5\leqslant 1091$ and $H_6\leqslant 15373$. Specifically, we apply certain generalizations of an approach by Papadoperakis, which essentially reduces the problem to the study of covering of $(n-2)$-dimensional faces of an $n$-dimensional cube by parallelepipeds of a particular form. A step in the construction of the required covering uses computer assistance. We also study limitations of this technique and establish some lower bounds on performance of this method.en_US
dc.language.isoengen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectHadwiger Covering Problemen_US
dc.titleOn Hadwiger covering problem in five- and six-dimensional Euclidean spacesen_US
dc.typeinfo:eu-repo/semantics/masterThesis
dc.typemaster thesisen_US
dc.degree.disciplineMathematicsen_US
dc.contributor.examiningcommitteeGunderson, Karen (Mathematics)en_US
dc.contributor.examiningcommitteeDurocher, Stephane (Computer Science)en_US
dc.degree.levelMaster of Mathematical, Computational and Statistical Sciences (M.M.C.S.S.)en_US
dc.description.noteMay 2022en_US


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