Can you hear the shape of a Beatty sequence?
| dc.creator | Graham, Ron | |
| dc.creator | O'Bryant, Kevin | |
| dc.date | 2008-08-31 | |
| dc.date.accessioned | 2026-07-07T09:59:36Z | |
| dc.date.available | 2026-07-07T09:59:36Z | |
| dc.description | Let K(x_1,...,x_d) be a polynomial. If you are not given the real numbers α_1, α_2, ...,α_d, but are given the polynomial K and the sequence a_n=K(\floor{nα_1},\floor{nα_2},...,\floor{nα_d}), can you deduce the values of α_i? Not, it turns out, in general. But with additional irrationality hypotheses and certain polynomials, it is possible. We also consider the problem of deducing α_i from the integer sequence with nested flooring (\floor{\floor{... \floor{\floor{nα_1}α_2}... α_{d-1}}α_d})_{n=1}^\infty. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0809.0004 | |
| dc.identifier | http://arxiv.org/abs/0809.0004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168081 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.title | Can you hear the shape of a Beatty sequence? | |
| dc.type | text |