On Hadwiger covering problem in five- and six-dimensional Euclidean spaces
| dc.contributor.author | Diao, Mingyang | |
| dc.contributor.examiningcommittee | Gunderson, Karen (Mathematics) | en_US |
| dc.contributor.examiningcommittee | Durocher, Stephane (Computer Science) | en_US |
| dc.contributor.supervisor | Prymak, Andriy | |
| dc.date.accessioned | 2022-03-31T20:04:54Z | |
| dc.date.available | 2022-03-31T20:04:54Z | |
| dc.date.copyright | 2022-03-16 | |
| dc.date.issued | 2022-03-16 | |
| dc.date.submitted | 2022-03-17T04:00:47Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Mathematical, Computational and Statistical Sciences (M.M.C.S.S.) | en_US |
| dc.description.abstract | We 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.description.note | May 2022 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/36378 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Hadwiger Covering Problem | en_US |
| dc.title | On Hadwiger covering problem in five- and six-dimensional Euclidean spaces | en_US |
| dc.type | master thesis | en_US |