Dyck Words, Lattice Paths, and Abelian Borders
We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We also extend to any number of di...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Open Publishing Association
2017-08-01
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Series: | Electronic Proceedings in Theoretical Computer Science |
Online Access: | http://arxiv.org/pdf/1708.06461v1 |
Summary: | We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We also extend to any number of distinct abelian borders a result of Rampersad et al. (Developments in Language Theory, 2013) on the exact number of binary words of a given length with no abelian borders. Furthermore, we generalize these results to partial words. |
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ISSN: | 2075-2180 |