Tomaszewského hypotéza
| Thesis title in Czech: | Tomaszewského hypotéza |
|---|---|
| Thesis title in English: | Tomaszewski conjecture |
| Key words: | pravděpodobnost;náhodné součty |
| English key words: | probability;random sum |
| Academic year of topic announcement: | 2019/2020 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Mgr. Robert Šámal, Ph.D. |
| Author: |
| 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. |