Palindromic complexity of infinite words associated with simple Parry numbers
| dc.creator | Ambrož, Petr | |
| dc.creator | Frougny, Christiane | |
| dc.creator | Masáková, Zuzana | |
| dc.creator | Pelantová, Edita | |
| dc.date | 2006-03-26 | |
| dc.date.accessioned | 2026-07-07T07:07:14Z | |
| dc.date.available | 2026-07-07T07:07:14Z | |
| dc.description | A simple Parry number is a real number β>1 such that the Rényi expansion of 1 is finite, of the form d_β(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_βthat are the fixed point of a substitution associated with a simple Parry number β. It is shown that the word u_βcontains infinitely many palindromes if and only if t_1=t_2= ... =t_{m-1} \geq t_m. Numbers βsatisfying this condition are the so-called confluent Pisot numbers. If t_m=1 then u_βis an Arnoux-Rauzy word. We show that if βis a confluent Pisot number then P(n+1)+ P(n) = C(n+1) - C(n)+ 2, where P(n) is the number of palindromes and C(n) is the number of factors of length n in u_β. We then give a complete description of the set of palindromes, its structure and properties. | |
| dc.description | 28 pages, to appear in Annales de l'Institut Fourier | |
| dc.identifier | https://arxiv.org/abs/math/0603608 | |
| dc.identifier | http://arxiv.org/abs/math/0603608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110318 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 68R15 (primary) 11A63 (secondary) | |
| dc.title | Palindromic complexity of infinite words associated with simple Parry numbers | |
| dc.type | text |