|
Título:
|
An extension of Christoffel duality to a subset of Sturm numbers and their characteristic words
|
|
Autores:
|
Castrillón López, Marco ;
Dominguez,, Manuel ;
Noll, Thomas
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
Elsevier Science, 2011
|
|
Dimensiones:
|
application/pdf
|
|
Nota general:
|
info:eu-repo/semantics/restrictedAccess
|
|
Idiomas:
|
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Matemáticas: Geometría
,
Tipo = Artículo
|
|
Resumen:
|
The paper investigates an extension of Christoffel duality to a certain family of Sturmian words. Given an Christoffel prefix w of length N of an Sturmian word of slope g we associate a N-companion slope g(N)* such that the upper Sturmian word of slope g(N)* has a prefix w* of length N which is the upper Christoffel dual of w. Although this condition is satisfied by infinitely many slopes, we show that the companion slope g(N)* is an interesting and somewhat natural choice and we provide geometrical and music-theoretical motivations for its definition. In general, the second-order companion (g(N)*)(N)* = g(N)** does not coincide with the original g. We show that, given a rational number 0 g(N)** has exactly one fixed point, phi(M/N) is an element of [0, 1), called odd mirror number. We show that odd mirror numbers are Sturm numbers and their continued fraction expansion is purely periodic with palindromic periods of even length. The semi-periods are of odd length and form a binary tree in bijection to the Farey tree of ratios 0
|
|
En línea:
|
https://eprints.ucm.es/id/eprint/14872/1/01.pdf
|
