Fourierova transformace na polytopech a dláždění obdélníky
| Thesis title in Czech: | Fourierova transformace na polytopech a dláždění obdélníky |
|---|---|
| Thesis title in English: | Fourier transform on polytopes and tiling with rectangles |
| Key words: | Fourierova transformace|polytop|dláždění |
| English key words: | Fourier transform|polytope|tiling |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | čeština |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 24.01.2022 |
| Date of assignment: | 24.01.2022 |
| Confirmed by Study dept. on: | 31.01.2022 |
| Date and time of defence: | 30.01.2023 08:00 |
| Date of electronic submission: | 04.01.2023 |
| Date of submission of printed version: | 09.01.2023 |
| Date of proceeded defence: | 30.01.2023 |
| Opponents: | Mgr. Martin Čech, Ph.D. |
| Advisors: | Mgr. Mikuláš Zindulka |
| Guidelines |
| Fourierova transformace charakteristické funkce polytopu zachycuje jeho geometrické a kombinatorické vlastnosti. Student využije Fourierovu transformaci k důkazu tvrzení o dláždění pomocí obdélníků, jejichž jedna strana je celočíselná. Následně se bude zabývat zobecněním do více dimenzí. |
| References |
| S. Robins: A friendly introduction to Fourier analysis on polytopes, arXiv: 2104.06407
N. G. de Bruijn: Filling boxes with bricks. Amer. Math. Monthly. 76 (1969), 37-40 S. Wagon: Fourteen Proofs of a Result About Tiling a Rectangle. Amer. Math. Monthly. 94 (1987), 601-617. |