2026-08-22T18:52:20Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/245412023-08-25T15:04:59Zcom_20.500.14352_14col_20.500.14352_15

Castrillón López, Marco Domínguez Romero, Manuel 2023-06-18T06:54:10Z 2023-06-18T06:54:10Z 2016 17459737 10.1080/17459737.2016.1164907 https://hdl.handle.net/20.500.14352/24541 http://www.tandfonline.com/doi/abs/10.1080/17459737.2016.1164907 http://www.tandfonline.com/ 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. eng restricted access LR property of non-well-formed scales journal article