# On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

2 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.
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Journal articles

Cited literature [15 references]

https://hal.archives-ouvertes.fr/hal-00580064
Contributor : Damien Jamet <>
Submitted on : Tuesday, March 29, 2011 - 10:55:13 AM
Last modification on : Wednesday, October 10, 2018 - 1:26:29 AM
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• HAL Id : hal-00580064, version 1

### Citation

Nicolas Bédaride, Eric Domenjoud, Damien Jamet, Jean-Luc Rémy. On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (3), pp.41-62. ⟨hal-00580064⟩

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