Tomaszewski's conjecture
| Thesis title in Czech: | Tomaszewského hypotéza |
|---|---|
| Thesis title in English: | Tomaszewski's conjecture |
| Key words: | pravděpodobnost;náhodné součty |
| English key words: | probability;random sum |
| Academic year of topic announcement: | 2016/2017 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Mgr. Robert Šámal, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 12.05.2017 |
| Date of assignment: | 12.05.2017 |
| Confirmed by Study dept. on: | 19.05.2017 |
| Date and time of defence: | 06.06.2018 00:00 |
| Date of electronic submission: | 11.05.2018 |
| Date of submission of printed version: | 11.05.2018 |
| Date of proceeded defence: | 06.06.2018 |
| Opponents: | Mgr. Jan Hladký, Ph.D. |
| Guidelines |
| Let v_1, v_2, . . . , v_n be real numbers such that the sum of their squares is at most 1. Consider the 2n signed sums of the form S = ±v_1 ± v_2 ± · · · ± v_n. In 1986, B. Tomaszewski asked the following question: is it always true that at least 1/2 of these sums satisfy |S| ≤ 1?
There have been a lot of partial results on this intriguing conjecture. The student will review the literature about the problem and work on (special cases of) the conjecture. |
| References |
| R. K. Guy. Any answers anent these analytical enigmas?. American Mathematical Monthly, 93(4):279–281, 1986.
R. Holzman and D. J. Kleitman. On the product of sign vectors and unit vectors. Combinatorica, 12(3):303–316, 1992. A další podle doporučení školitele. |