Abstract
In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in ℤ not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a 3-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we study the lengths of the abelian unbordered factors occurring in the Thue-Morse word. © 2013 Springer-Verlag.
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CITATION STYLE
Rampersad, N., Rigo, M., & Salimov, P. (2013). On the number of abelian bordered words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7907 LNCS, pp. 420–432). https://doi.org/10.1007/978-3-642-38771-5_37
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