RT Journal Article
T1 LR property of non-well-formed scales
A1 Castrillón López, Marco
A1 Domínguez Romero, Manuel
AB This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be naturally inserted in the Christoffel tree of well-formed words. Our primary focus in this study is on the left- and right-Lyndon factorization of these words. We will characterize the non-well-formed words for which both factorizations coincide. We say that these words satisfy the LR property and show that the LR property is satisfied exactly for half of the non-well-formed words. These are symmetrically distributed in the extended Christoffel tree. Moreover, we find a surprising connection between the LR property and the Christoffel duality. Finally, we prove that there are infinitely many Christoffel–Lyndon words among the set of non-well-formed words and thus there are infinitely many generated scales having as step-pattern a Christoffel–Lyndon word.
PB Taylor Francis
SN 17459737
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24541
UL https://hdl.handle.net/20.500.14352/24541
LA eng
DS Docta Complutense
RD 17 may 2024