LR property of non-well-formed scales
Data(s) |
2016
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Idioma(s) |
en |
Publicador |
Taylor Francis |
Relação |
http://eprints.ucm.es/38182/ http://www.tandfonline.com/doi/abs/10.1080/17459737.2016.1164907 http://dx.doi.org/10.1080/17459737.2016.1164907 |
Direitos |
info:eu-repo/semantics/restrictedAccess |
Palavras-Chave | #Matemáticas |
Tipo |
info:eu-repo/semantics/article PeerReviewed |