Combinatorial and Arithmetical Properties of Infinite Words Associated with Non-simple Quadratic Parry Numbers
| dc.creator | Balková, Lubomíra | |
| dc.creator | Pelantová, Edita | |
| dc.creator | Turek, Ondřej | |
| dc.date | 2006-08-16 | |
| dc.date | 2006-08-17 | |
| dc.date.accessioned | 2026-07-07T07:20:00Z | |
| dc.date.available | 2026-07-07T07:20:00Z | |
| dc.description | We study arithmetical and combinatorial properties of $β$-integers for $β$ being the root of the equation $x^2=mx-n, m,n \in \mathbb N, m \geq n+2\geq 3$. We determine with the accuracy of $\pm 1$ the maximal number of $β$-fractional positions, which may arise as a result of addition of two $β$-integers. For the infinite word $u_β$ coding distances between consecutive $β$-integers, we determine precisely also the balance. The word $u_β$ is the fixed point of the morphism $A \to A^{m-1}B$ and $B\to A^{m-n-1}B$. In the case $n=1$ the corresponding infinite word $u_β$ is sturmian and therefore 1-balanced. On the simplest non-sturmian example with $n\geq 2$, we illustrate how closely the balance and arithmetical properties of $β$-integers are related. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/cs/0608065 | |
| dc.identifier | http://arxiv.org/abs/cs/0608065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114835 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | D.3.1 | |
| dc.title | Combinatorial and Arithmetical Properties of Infinite Words Associated with Non-simple Quadratic Parry Numbers | |
| dc.type | text |