Palindromic complexity of infinite words associated with simple Parry numbers

dc.creatorAmbrož, Petr
dc.creatorFrougny, Christiane
dc.creatorMasáková, Zuzana
dc.creatorPelantová, Edita
dc.date2006-03-26
dc.date.accessioned2026-07-07T07:07:14Z
dc.date.available2026-07-07T07:07:14Z
dc.descriptionA 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.description28 pages, to appear in Annales de l'Institut Fourier
dc.identifierhttps://arxiv.org/abs/math/0603608
dc.identifierhttp://arxiv.org/abs/math/0603608
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110318
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject68R15 (primary) 11A63 (secondary)
dc.titlePalindromic complexity of infinite words associated with simple Parry numbers
dc.typetext

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